Answer: Use either the slopeintercept form (from Section 3.5) or the pointslope form

(7, 1) is called an _____ pair.

In the ordered pair (2, 5), the -coordinate is 2 and the y- ______ is -5.

A rectangular coordinate system is formed by two perpendicular number lines called the x - ______ and the y- _____. The point where the axes cross is called the ______ .

The x- and y-axes divide the coordinate plane into four regions called ______ .

The point with coordinates (4, 2) can be graphed on a ______ coordinate system.

The process of locating the position of a point on a coordinate plane is called ______ the point.

a. To plot (5, 4), we start at the ____ and move 5 units to the _____ and then move 4 units ____ . b. To plot 16, 3 2 2, we start at the ____ and move 6 units to the ____ and then move 3 2 units ______ .

In which quadrant is each point located? a. (2, 7) 2 b. 1 1 2, 15 16 c. (1, 2.75) (5 d. (50, 16)

a. In which quadrants are the second coordinates of points positive? b. In which quadrants are the first coordinates of points negative? c. In which quadrant do points with a positive -coordinate and a negative -coordinate lie? d. On what axis are the first coordinates of points zero?

Farming. The number of bushels of wheat produced per acre depends on the amount of water it receives. Plot the data in the table as ordered pairs and draw a straight line through the points. Use the graph to determine how many bushels per acre will be produced if a. 6 inches of rain fall. b. 10 inches of rain fall. Inches Bushels of rain per acre 2 20 4 30 8 50 y 123 Rain (in.) Bushels produced per acre 4 5 6 7 8 9 10 10 20 30 40 50 60 70

Explain the difference between (3, 5) and 3(5).

In a paired-data table, does the first or second column contain values associated with the vertical axis of a graph?

Do these ordered pairs name the same point? 2.5, , 2 7 2 2, 2 2 1 2 1, , 3.52 7, 12.5, 31 2 12 2 1

Do (3, 2) and (2, 3) represent the same point?

In the ordered pair (4, 5), is the number 4 associated with the horizontal or the vertical axis?

Fill in the blank: In the notation , the capital letter is used to name a _____ .

Plot each point: (3, 4), (4, 3.5), 12, 5 2 2, (0, 4), 1 3 2, 02, (2.7, 4.1) P(4,

Plot each point: (4, 4), (0.5, 3), (3.9, 3.2), (0, 1), (0, 0), (0, 3), (2, 0) (3,

Complete the coordinates for each point in figure (a) below. a. y x (?, 0) (?, 3) (0, ?) (4, ?) (4, ?) 1 1 1 1 2 3 4 2 3 4 4 2 3 2 3 b. x A B C D F E 111 1 2 3 4 2 3 4 234 2 3 4 5

Find the coordinates of points A, B, C, D, E and F in figure (b) above.

The following graph gives the heart rate of a woman before, during, and after an aerobic workout. Use it to answer Problems 2124. See Example 3. y Training Cooling down Warming up 10010 60 80 40 20 100 120 140 160 20 30 Time (min) Heart rate (beats/min) 40 50 60 a. What was her heart rate before beginning the workout? b. After beginning her workout, how long did it take the woman to reach her training-zone heart rate?

The following graph gives the heart rate of a woman before, during, and after an aerobic workout. Use it to answer Problems 2124. See Example 3. y Training Cooling down Warming up 10010 60 80 40 20 100 120 140 160 20 30 Time (min) Heart rate (beats/min) 40 50 60 a. What was the womans heart rate half an hour after beginning the workout? b. For how long did the woman work out at her training zone?

The following graph gives the heart rate of a woman before, during, and after an aerobic workout. Use it to answer Problems 2124. See Example 3. y Training Cooling down Warming up 10010 60 80 40 20 100 120 140 160 20 30 Time (min) Heart rate (beats/min) 40 50 60 a. At what time was her heart rate 100 beats per minute? b. How long was her cool-down period?

The following graph gives the heart rate of a woman before, during, and after an aerobic workout. Use it to answer Problems 2124. See Example 3. y Training Cooling down Warming up 10010 60 80 40 20 100 120 140 160 20 30 Time (min) Heart rate (beats/min) 40 50 60 a. What was the difference in the womans heart rate before the workout and after the cool-down period? b. What was her approximate heart rate 8 minutes after beginning?

The following graph shows the depths of a submarine at certain times after it leaves port. Use the graph to answer Problems 2528. See Example 3. d Depth of submarine (ft) 2,500 2,000 1,500 1,000 500 0 500 Hours after leaving port 1234 567 8 a. For how long does the sub travel at sea level? b. What is the depth of the sub 5 hours after leaving port?

The following graph shows the depths of a submarine at certain times after it leaves port. Use the graph to answer Problems 2528. See Example 3. d Depth of submarine (ft) 2,500 2,000 1,500 1,000 500 0 500 Hours after leaving port 1234 567 8 a. Once the sub begins to dive, how long does it take to reach feet in depth? b. For how long does the sub travel at a depth of 1,000 feet?

The following graph shows the depths of a submarine at certain times after it leaves port. Use the graph to answer Problems 2528. See Example 3. d Depth of submarine (ft) 2,500 2,000 1,500 1,000 500 0 500 Hours after leaving port 1234 567 8 a. Explain what happens 6 hours after the sub leaves port. b. What is the depth of the sub 8 hours after leaving port?

The following graph shows the depths of a submarine at certain times after it leaves port. Use the graph to answer Problems 2528. See Example 3. d Depth of submarine (ft) 2,500 2,000 1,500 1,000 500 0 500 Hours after leaving port 1234 567 8 a. How long does it take the sub to first reach feet in depth? b. Approximate the time when the sub reaches feet in depth for the second time

Bridge Construction. Find the coordinates of each rivet, weld, and anchor. Weld Rivet Rivet Weld x y Anchor Anchor

Golf. A golfer is videotaped and then has her swing displayed on a computer monitor so that it can be analyzed. Give the coordinates of the three highlighted points in red. 6 3 3 6 12 x y

Games. In the game Battleship, players use coordinates to drop depth charges from their ships to hit submarines. What coordinates should be used to make three hits on the submarine seen here? Express each answer in the form (letter, number). A 0 1 2 3 4 5 6 7 BCDE FGH I J

Maps. Use coordinates of the form (number, letter) to locate each of the following on the map: Tempe, Glendale, Paradise Valley, Sky Harbor Airport, and the intersection of Camelback Road and 7th Avenue. A B C D E 1 2 34 5 67 8 Bethany Home Rd Glendale Ave Northern Ave Camelback Rd Indian School Rd ThomasRd Lincoln Dr McDonald Dr McDowell Rd Van Buren St Buckeye Rd University DrHayden Rd Scottsdale Rd 43rd Ave 35rd Ave 27rd Ave 19th Ave 7th Ave Central Ave 16th St Tatum Blvd 24th St 40th St

Dental Assistant Dentists describe teeth as being located in one of four quadrants as shown above. a. How many teeth are in each quadrant? b. Why would the upper left quadrant appear on the right in the illustration? Upper left quadrant Lower left quadrant Upper right quadrant Midline Lower right quadrant

Geography. A coordinate system that describes the location of any place on the surface of the Earth uses a series of latitude and longitude lines, as shown below. Estimate the location of the Deep Water Horizon (the oil drilling rig in the Gulf of Mexico that exploded in 2010) using an ordered pair of the form (latitude, longitude). (Source: sailwx.info) Deep Water Horizon Oil Rig 125 120 115 110 105 100 95 90 85 80 75 70 45

Water Pressure. The graphs show how the path of a stream of water changes when the hose is held at two different angles. a. At which angle does the stream of water shoot up higher? How much higher? b. At which angle does the stream of water shoot out farther? How much farther?Nozzle held at 60 angle 1 1 2 4 5 7 6 12345 23 4 567

Area. Three vertices (corners) of a rectangle are (2, 1), (6, 1) and (6, 4). Find the coordinates of the fourth vertex. Then find the area of the rectangle.

Area. Three vertices (corners) of a right triangle are (-1, -7), (-5, -7), and (-5, -2). Find the area of the triangle.

Landmarks. A scale model of the block letter H in the Hollywood sign can be drawn by plotting the following points and connecting them: (0, 0), (13, 0), (13, 16), (26, 16), (26, 0), (39, 0), (39, 45), (26, 45), (26, 29), (13, 29), (13, 45), and (0, 45). The scale is 1 unit on the graph is equal to 1 foot on the actual sign. If a gallon of paint covers 350 square feet, how many gallons are needed to paint the front side of the letter H? Round to the nearest gallon.

Trucks. The table below shows the number of miles that an 18-wheel truck can be driven on a given number of gallons of diesel fuel. Plot the data in the table as ordered pairs. Then draw a straight line through the points. a. How far can the truck go on 4 gallons of fuel? b. How many gallons of fuel are needed to travel a distance of 30 miles? c. How far can the truck go on 7 gallons of fuel?Fuel Distance (gal) (mi) 2 10 3 15 5 25 5 10 15 20 25 30 40 35 2345678 Diesel fuel used (gal) Distance traveled (mi) y

Boating. The table below shows the cost to rent a sailboat for a given number of hours. Plot the data in the table as ordered pairs. Then draw a straight line through the points. a. What does it cost to rent the boat for 3 hours? b. For how long can the boat be rented for $60? c. What does it cost to rent the boat for 9 hours? Rental Cost time (hr) ($) 2 20 4 30 6 40 1 10 20 30 40 50 60 70 80 2 3 4 5 6 7 8 9 10 Rental time (hr) Rental cost ($) y

Depreciation. The table below shows the value (in thousands of dollars) of a color copier at various lengths of time after its purchase. Plot the data in the table as ordered pairs. Then draw a straight line passing through the points. a. What does the point on the graph tell you? b. Find the value of the copier when it is 7 years old. c. After how many years will the copier be worth $2,500? Age Value (yr) ($1,000) 3 7 4 5.5 5 4 1 1 2 3 4 5 6 7 8 9 10 11 12 2345678 Age of copier (years) Thousands of dollars y

Swimming. The table below shows the number of people at a public swimming pool at various times during the day. (0 represents noon, 1 represents 1 PM, and so on.) Plot the data in the table as ordered pairs. Then draw a straight line passing through the points. a. How many people will be at the pool at 6 P.M.? b. At what time will there be 250 people at the pool? c. At what time will the number of people at the pool be half of what it was at noon? Number Time of people 0 350 3 200 5 100 100 0 200 300 400 2345678 Time of day (PM) Number of people y

Explain why the point (-3, 3) is not the same as the point (3, -3).

Explain how to plot the point (-2, 5).

Use the Internet to perform a search of the name Ren Descartes. After reading about him, explain how a fly on his bedroom ceiling provided the inspiration for the concept of a rectangular coordinate system.

Explain this diagram. II (, +) I (+, +) III (, ) IV (+, )

Solve AC h 2 3h T for h.

Solve 5(x  1)  2(x 3). Write the solution set in interval notation and graph it.

Evaluate: 4(4  2) 23 0 12 4(5) 0 5(x

Simplify: 24 54

In what quadrant does a point lie if the sum of its coordinates is negative and the product of its coordinates is positive?

Draw line segment AB with endpoints A(6, 5) and B(4, 5). Suppose that the x-coordinate of a point C is the average of the x-coordinates of points A and B, and the y-coordinate of point is the average of the y-coordinates of points A and B. Find the coordinates of point C. Why is called the midpoint of AB?

y = 9x + 5 is an equation in _____ variables, x and y.

A _____ of an equation in two variables is an ordered pair of numbers that makes the equation a true statement.

Solutions of equations in two variables are often listed in a ______ of solutions.

The line that represents all of the solutions of a linear equation is called the ______ of the equation.

y = 3x + 8 is a equation ______ and its graph is a line.

The _____ form of a linear equation in two variables is Ax + By = C.

Consider: y = - 3x + 6. a. How many variables does the equation contain? b. Does (4, 6) satisfy the equation? c. Is (2, 0) a solution of the equation? d. How many solutions does this equation have?

To graph a linear equation, three solutions were found, they were plotted (in black), and a straight line was drawn through them, as shown below. a. Looking at the graph, complete the table of solutions. b. From the graph, determine three other solutions of the equation. 1 ( , ) 1 ( , ) 4 ( , ) yx (x y x 1 1 3 4 5 1 2 3 4 5 2345

The graph of y = -2x - 3 is shown in Problem 8. Fill in the blanks: Every point on the graph represents an ordered-pair _____ of y = -2x - 3 and every ordered-pair solution is a _____ on the graph.

The graph of a linear equation is shown. a. If the coordinates of point are substituted into the equation, will the result be true or false? b. If the coordinates of point are substituted into the equation, will the result be true or false? y N(1, 1) M(2, 3) 1 1 3 4 1 2 3 2 2 134

Suppose you are making a table of solutions for each given equation. What three -values would you select to make the calculations for finding the corresponding -values the easiest? a. y  4 5 x  2 b. y 0.6x  500 4

A table of solutions for a linear equation is shown below. When constructing the graph of the equation, how would you scale the -axis and the -axis? 600 5 100 35 (35, 500 500) (5, 100) 20 (20, 600) yx (x,

Complete each solution. Verify that is a solution of y x  4 6. 6 6  4 ( )  4 y x  4 (2, 6

Complete each solution. Solve 5x  3y 15 for y. 5x  3y 5x   15 5x  15 5 3y 5x  15 y x 

a. In the linear equation y 1 2 x  7 what are the understood exponents on the variables? b. Explain why y y2  2 y and y x3 y 4are not linear equations.

Complete the labeling of the table of solutions and the axes of the graph of c a  4. (,) 5 0 4 2 2 (2, 2) (0, 4) 1 (1, 5) G 6 1 2 2 2 1 2 3 4 65

Determine whether each equation has the given ordered pair as a solution. See Example 1. y 5x 4; (1, 1) y

Determine whether each equation has the given ordered pair as a solution. See Example 1. y 2x  3; (2, 1)c

Determine whether each equation has the given ordered pair as a solution. See Example 1. 7x 2y 3; (2, 6) 10

Determine whether each equation has the given ordered pair as a solution. See Example 1. 10x y 10; (0, 0)y

Determine whether each equation has the given ordered pair as a solution. See Example 1. x  12y 12; (0, 1) 2x

Determine whether each equation has the given ordered pair as a solution. See Example 1. 2x  3y 0; (3, 2) 7x

Determine whether each equation has the given ordered pair as a solution. See Example 1. 3x 6y 12; (3.6, 3.8) x 

Determine whether each equation has the given ordered pair as a solution. See Example 1. 8x  4y 10; (0.5, 3.5) 3

Determine whether each equation has the given ordered pair as a solution. See Example 1. y 6x 12; 1 , 22 5 6, 72 8

Determine whether each equation has the given ordered pair as a solution. See Example 1. y  8x 4; 1 3 4 ; 1 , 22 5

Determine whether each equation has the given ordered pair as a solution. See Example 1. y (8, 12) 3 4 x  8 y 

Determine whether each equation has the given ordered pair as a solution. See Example 1. y (12, 4) 1 6 x 2 3 4

For each equation, complete the solution. See Example 2. y 5x 4; (3, ) y 8x

For each equation, complete the solution. See Example 2. y 8x  30; (6, ) y

For each equation, complete the solution. See Example 2. 4x 5y 4; ( , 4) 7x

For each equation, complete the solution. See Example 2. 7x  y 12; ( , 2) y

For each equation, complete the solution. See Example 2. y ) x 4  9; (16, ) 4x

For each equation, complete the solution. See Example 2. y x 6 y 8; (48, ) x 4

For each equation, complete the solution. See Example 2. 7x 4y; 1 , 22 11

For each equation, complete the solution. See Example 2. 11x 16y; 1 , 32 y

Complete each table of solutions. See Example 3. y 2x 4 38

Complete each table of solutions. See Example 3. y 3x  1 7

Complete each table of solutions. See Example 3. 3x y  2

Complete each table of solutions. See Example 3. 5x 2y  15

Construct a table of solutions and then graph each equation. See Example 4. y 2x 3 y

Construct a table of solutions and then graph each equation. See Example 4. y 3x  12

Construct a table of solutions and then graph each equation. See Example 4. y 5x 4 y

Construct a table of solutions and then graph each equation. See Example 4. y 6x 3y

Construct a table of solutions and then graph each equation. See Example 5. y 6x y

Construct a table of solutions and then graph each equation. See Example 5. y 2xy

Construct a table of solutions and then graph each equation. See Example 5. y 7x y

Construct a table of solutions and then graph each equation. See Example 5. y 8x y

Solve each equation for y and then graph it. See Example 6. 2x  3y 3 2x

Solve each equation for y and then graph it. See Example 6. 2x  3y 9

Solve each equation for y and then graph it. See Example 6. 5y x 20 4y

Solve each equation for y and then graph it. See Example 6. 4y x 8 2

Graph each equation. Solve for y first, when necessary. y x y

Graph each equation. Solve for y first, when necessary. y 4x

Graph each equation. Solve for y first, when necessary. y x 1 y x

Graph each equation. Solve for y first, when necessary. y x  2y

Graph each equation. Solve for y first, when necessary. 3y 12x  15 5

Graph each equation. Solve for y first, when necessary. 5y 20x 30 y

Graph each equation. Solve for y first, when necessary. y x  2 3 8 x 6 3

Graph each equation. Solve for y first, when necessary. y 3 2 y x  2 3

Graph each equation. Solve for y first, when necessary. y 1.5x 4 y

Graph each equation. Solve for y first, when necessary. y 0.5x  3

Graph each equation. Solve for y first, when necessary. 8x  4y 16 1

Graph each equation. Solve for y first, when necessary. 14x  7y 28

Graph each equation. Solve for y first, when necessary. y x 1 2 x 8

Graph each equation. Solve for y first, when necessary. y 3 4 y x 1

Graph each equation. Solve for y first, when necessary. y x 2 5 6 x 5 y

Graph each equation. Solve for y first, when necessary. y 2 3 y x 2 5

Graph each equation. Solve for y first, when necessary. 6y 30x  12 3y

Graph each equation. Solve for y first, when necessary. 3y 9x 15 y

Graph each equation. Solve for y first, when necessary. y 1 x 3 6

Graph each equation. Solve for y first, when necessary. y x 3 y 1 x 3

Graph each equation. Solve for y first, when necessary. y 2x  1 y

Graph each equation. Solve for y first, when necessary. y 3x  2 y

Graph each equation. Solve for y first, when necessary. 7x y 1 2x

Graph each equation. Solve for y first, when necessary. 2x y 3 y

Graph each equation. Solve for y first, when necessary. 7y 2x 6y

Graph each equation. Solve for y first, when necessary. 6y 4x 7

Graph each equation. Solve for y first, when necessary. y 2.5x  5 y

Graph each equation. Solve for y first, when necessary. y 3.5x  4 7

Billiards. The path traveled by the black 8-ball is described by the equations y 2x 4 y and y 2x  12y. Construct a table of solutions for y 2x 4 x using the x-values 1, 2, and 4. Do the same for y 2x  12 x, using the x-values 4, 6, and 8. Then graph the path of the 8-ball. y 2 2 2 246 4 6

Ping-Pong. The path traveled by a Ping-Pong ball is described by the equations y 1 2 x  3 2 and y 1 2 x 3 2 y .Construct a table of solutions for y x 1 2 x  3 2 using the x-values 7, 3, and . Do the same for y x 3, 5 1 2 x 3 2 3 y, using the x-values 3, 5, and 7. Then graph the path of the ball. 5 5 5 4 y

Defrosting Poultry. The number of hours needed to defrost a turkey weighing pounds in the refrigerator can be estimated by h = 5p. Graph the equation and use the graph to estimate the time needed to defrost a 25-pound turkey. (Source: helpwithcooking.com.)

Owning a Car. In 2010, the average cost (in dollars) to own and operate a car was estimated by c = 0.57m, where m represents the number of miles driven. Graph the equation and use the graph to estimate the cost in 2010 of operating a car that is driven 25,000 miles. (Source: AAA Auto Club)

Housekeeping. The linear equation A = -0.02n + 16 estimates the amount of furniture polish (in ounces) that is left in the bottle after the sprayer trigger has been pulled a total of times. Graph the equation and use the graph to estimate the amount of polish that is left after 650 sprays.

Sharpening Pencils. The linear equation L 0.04t  8 n estimates the length (in inches) of a pencil after it has been inserted into a sharpener and the handle turned a total of t times. Graph the equation and use the graph to estimate the length of the pencil after 75 turns of the handle. L in. t turns of the handle

NFL Tickets. The average ticket price to a National Football League game during the years 19902009 is approximated by p 2.7t  20, where is the number of years after 1990. Graph this equation and use the graph to predict the average ticket price in 2020. (Source: Team Marketing Report, NFL.)

U.S. Automobile Accidents. The number of lives saved by seat belts during the years 20002009 is estimated by n 170t  13,800, where is the number of years after 2000. Graph this equation and use the graph to predict the number of lives that will be saved by seat belts in 2015. (Source: NHTSA National Center for Statistics.) 8

Raffles. A private school is going to sell raffle tickets as a fund raiser. Suppose the number of raffle tickets that will be sold is predicted by the equation n = -20p + 300, where is the price of a raffle ticket in dollars. Graph the equation and use the graph to predict the number of raffle tickets that will be sold at a price of $6.

Endangered Species. The number n of endangered plant and animal species in the U.S. during the years 20002010 is estimated by n 9t  960, where t is the number of years after 2000. Graph this equation and use the graph to predict the number of endangered species in the U.S. in 2022. (Source: The World Almanac and Book of Facts, 2010).

U.S. Space Program. Since 1980, the Gallup Poll organization has surveyed Americans to see whether they think the space program has brought enough benefits to the country to justify its cost. The percent p responding yes is estimated by p 3 5t  40, where t is the number of years after 1980. Graph the equation. If the polling trend continues, when will the percent that respond yes reach 70%? (Source: galluppoll.com)

Gas Mileage. The mileage for a Honda Insight traveling between 55 mph and 75 mph is estimated by the equation m 3 4s  95 p, where s is the speed of the car (in mph) and m is the mileage (in miles per gallon). Graph the equation for s between 55 and 75. Estimate the speed at which the mileage of the car drops below 40 miles per gallon. (Source: Consumer Reports 9/10/2009) 55 35 40 45 50 55 60 65 70 75 Miles per hour (mph) Miles per gallon (mpg) m. The symbol is used to show the break in the scale on an axis. Such a break enables us to omit large portions of empty space on a graph.

When we say that (-2, -6) y is a solution of y = x - 4, what do we mean?

What is a table of solutions?

What does it mean when we say that a linear equation in two variables has infinitely many solutions?

A linear equation and a graph are two ways of describing a relationship between two quantities. Which do you think is more informative and why?

From geometry, we know that two points determine a line. Why is it a good practice when graphing linear equations to find and plot three solutions instead of just two?

A student found three solutions of a linear equation in two variables and plotted them as shown. What conclusion can be made about the location of the points? y (3, 4) (2, 2) (3, 2) 1 1 3 4 1 2 2 3 4 234 1 2 3

graph , one student made the table of solutions on the left. Another student made the table on the right. The tables are different. Could they both be correct? Explain. 1 2 (1, 2) 1 4 (1, 4) 2 7 (2, 7) yx (x, y) 0 2 5 3 8 (3, 8) (2, 5) 1 (0, 1) yx (x, y) 99

Both graphs below are of the same linear equation . Why do the graphs have a different appearance? y x y 1 15 20 5 10 10 15 20 234 1 2 3 4 1 30 40 10 20 20 30 40 234 1 2 3 4

Simplify: (5 4c)y

Write the set of integers.

Find the volume, to the nearest tenth of a cubic foot, of a sphere with radius 6 feet.

Solve: 2(a  3) 3(a 5) (5

Graph each of the following nonlinear equations in two variables by constructing a table of solutions consisting of seven ordered pairs. These equations are called nonlinear, because their graphs are not straight lines. y x 2 2  12

Graph each of the following nonlinear equations in two variables by constructing a table of solutions consisting of seven ordered pairs. These equations are called nonlinear, because their graphs are not straight lines. y x3 2 

Graph each of the following nonlinear equations in two variables by constructing a table of solutions consisting of seven ordered pairs. These equations are called nonlinear, because their graphs are not straight lines. y 0 x 0 2 y

Graph each of the following nonlinear equations in two variables by constructing a table of solutions consisting of seven ordered pairs. These equations are called nonlinear, because their graphs are not straight lines. y (x  2)2

The _____ of a line is the point where the line intersects/crosses the -axis.

The y-intercept of a line is the point where the line _____ the y-axis.

The graph of y = 4 is a ____ line and the graph of x = 6 is a ____ line.

The intercept method is useful when graphing linear equations written in the _____ form Ax + By = C.

Fill in the blanks. a. To find the y-intercept of the graph of a line, substitute for x in the equation and solve for . b. To find the x-intercept of the graph of a line, substitute for in the equation and solve for .

Complete the table of solutions and fill in the blanks. 3x  2y 6 0 2 yx ( -intercept -intercept point 3x

a. Refer to the graph. Which intercept tells the purchase price of the machinery? What was that price? b. Which intercept indicates when the machinery will have lost all of its value? When is that? y 100 20,000 40,000 60,000 80,000 100,000 120,000 20 30 40 50 60 Age of machinery (years)

Match each graph with its equation. a. x 2 y b. y 2 y c. y 2x d. 2x y 2 y e. y 2x  2 y f. y 2xx i. ii. x y 1 34 1 2 3 4 3 2 4 1 4 3 12 x y 1234 1 2 3 4 3 2 4 1 4 3 12

What is the equation of the x-axis? What is the equation of the y-axis?

Write the coordinates that are improper fractions as mixed numbers. a. 1 2 7 2, 02 b. 10, 17 3 1 2 7

Give the coordinates of the intercepts of each graph. See Example 1. y 1 3 2 4 1 3 2 4 3 2 4 1 4 3

Give the coordinates of the intercepts of each graph. See Example 1. y 1 3 2 4 1 3 2 4 3 2 4 1 4 3

Give the coordinates of the intercepts of each graph. See Example 1. y 1 2 1 3 2 4 6 5 7 1 6 5 4 3 1

Give the coordinates of the intercepts of each graph. See Example 1. y 1 3 2 1 3 2 4 3 2 4 1 46 3 1

Give the coordinates of the intercepts of each graph. See Example 1. y 1 3 2 4 1 3 4 3 2 4 1 4 3

Give the coordinates of the intercepts of each graph. See Example 1. y 1 3 2 4 1 3 2 4 3 2 4 1 4 3 12

Estimate the coordinates of the intercepts of each graph. (Some are not integers.) See Example 1. (Answers may vary.) y 1 1 1 1 2 2

Estimate the coordinates of the intercepts of each graph. (Some are not integers.) See Example 1. (Answers may vary.) y 1 1 1 1

Find the x- and y-intercepts of the graph of each equation. Do not graph the line. See Example 2. 8x  3y 24 5

Find the x- and y-intercepts of the graph of each equation. Do not graph the line. See Example 2. 5x  6y 30

Find the x- and y-intercepts of the graph of each equation. Do not graph the line. See Example 2. 7x 2y 28 2x

Find the x- and y-intercepts of the graph of each equation. Do not graph the line. See Example 2. 2x 9y 36 8

Find the x- and y-intercepts of the graph of each equation. Do not graph the line. See Example 2. 5x 3y 10 9x

Find the x- and y-intercepts of the graph of each equation. Do not graph the line. See Example 2. 9x 5y 25 7x

Find the x- and y-intercepts of the graph of each equation. Do not graph the line. See Example 2. 6x  y 9 x

Find the x- and y-intercepts of the graph of each equation. Do not graph the line. See Example 2. x  8y 14

Use the intercept method to graph each equation. See Example 2. 4x  5y 20 3

Use the intercept method to graph each equation. See Example 2. 3x  4y 12

Use the intercept method to graph each equation. See Example 2. 5x  15y 15 8x

Use the intercept method to graph each equation. See Example 2. 8x  4y 24 4

Use the intercept method to graph each equation. See Example 2. x y 3 x

Use the intercept method to graph each equation. See Example 2. x y 3 5

Use the intercept method to graph each equation. See Example 2. x  2y 2 x

Use the intercept method to graph each equation. See Example 2. x  2y 4 x

Use the intercept method to graph each equation. See Example 3. 30x  y 30 20

Use the intercept method to graph each equation. See Example 3. 20x y 20 x

Use the intercept method to graph each equation. See Example 3. 4x 20y 60 6x

Use the intercept method to graph each equation. See Example 3. 6x 30y 30 3

Use the intercept method to graph each equation. See Example 4. 3x  4y 8 2

Use the intercept method to graph each equation. See Example 4. 2x  3y 9

Use the intercept method to graph each equation. See Example 4. 9x  4y 9 5x

Use the intercept method to graph each equation. See Example 4. 5x  4y 15 3

Use the intercept method to graph each equation. See Example 4. 3x 4y 11 5x

Use the intercept method to graph each equation. See Example 4. 5x 4y 13 9

Use the intercept method to graph each equation. See Example 4. 9x  3y 10 4

Use the intercept method to graph each equation. See Example 4. 4x  4y 5

Use the intercept method to graph each equation. See Example 5. 3x  5y 0 4

Use the intercept method to graph each equation. See Example 5. 4x  3y 0

Use the intercept method to graph each equation. See Example 5. 2x 7y 0 6x

Use the intercept method to graph each equation. See Example 5. 6x 5y 0 3

Graph each equation. See Examples 6 and 7. y 5 y

Graph each equation. See Examples 6 and 7. y 3 2

Graph each equation. See Examples 6 and 7. y 0 x

Graph each equation. See Examples 6 and 7. x 0

Graph each equation. See Examples 6 and 7. x 2 x

Graph each equation. See Examples 6 and 7. x 5

Graph each equation. See Examples 6 and 7. x 4 3

Graph each equation. See Examples 6 and 7. y 1 2 x

Graph each equation. See Examples 6 and 7. y 2 0 y (Hint: Solve for first.)

Graph each equation. See Examples 6 and 7. x  1 0 x (Hint: Solve for first.)

Graph each equation. See Examples 6 and 7. 5x 7.5 x (Hint: Solve for first.)

Graph each equation. See Examples 6 and 7. 3y 4.5 (Hint: Solve for first.)

Graph each equation. 7x 4y 12 7x

Graph each equation. 7x 5y 15 8

Graph each equation. 4x 3y 12 5x

Graph each equation. 5x 10y 20 7

Graph each equation. x 5 3 4

Graph each equation. y 5 2 x

Graph each equation. y 3x 4 3 y

Graph each equation. y 2x 9 8 y

Graph each equation. 7x  3y 0 4

Graph each equation. 4x 5y 0 y

Graph each equation. 4x 8 2y 5x

Graph each equation. 5x 10  5y 7

Graph each equation. 3x 150 5y x

Graph each equation. x 50 5y 4

Graph each equation. 3y 3 2

Graph each equation. 2x 8 3x

Chemistry. The relationship between the temperature and volume of a gas kept in a sealed container at a constant pressure is graphed below. The -intercept of this graph is a very important scientific fact. It represents the lowest possible temperature, called absolute zero. a. Estimate absolute zero. b. What is the volume of the gas when the temperature is absolute zero? V Degrees Celsius milliliters Absolute zero T 500 250 300 350 200 150 100 50 300 50100150200250

Physics. The graph shows the length of a stretched spring (in inches) as different weights (in pounds) are attached to it. What information about the spring does the -intercept give? L in. w pounds 0.5 1.0 1.5 2.0 2.5 3.0 0 5 10 15 Pounds

Bottled Water Dispenser. The graph below shows the number of gallons g of water remaining in a bottle after c six-ounce cups have been served from it. Find the intercepts of the graph. What information do they give? 25 50 75 100 125 Number of six-ounce cups served Water in bottle (gal) 1 2 3 4 5 15c + 320g = 1,600 g

Renewable Energy. The equation p = 50s - 300 estimates the power output in watts from a propeller blade turbine driven by a wind of speed s miles per hour. What information does the s-intercept of the graph of the equation give? (Source: otherpower.com)

Landscaping. A developer is going to purchase trees and shrubs to landscape a new office complex. The trees cost $50 each and the shrubs cost $25 each. His budget is $5,000. This situation is modeled by the equation 50x + 25y = 5,000. Use the intercept method to graph it. a. What information is given by the y-intercept? b. What information is given by the x-intercept?

Eggs. The number of eggs eaten by an average American in one year has remained almost constant since the year 2000. See the graph below. Draw a horizontal line that passes through, or near, the data points. What is the equation of the line? 00 0 5 1 2 3 4 Years after 2000 Source: United Egg Number of eggs eaten per person in the U.S. n t 252 253 254 254 257 255 6 258 7 251 8 248 9 247 10 246

To graph 3x  2y 12, a student found the intercepts and a check point, and graphed them, as shown in figure (a). Instead of drawing a crooked line through the points, what should he have done?y x y x (0, 4) (a) (b) 11 1 1 2 3 4 2 3 4 234 2 3 4 11 1 1 2 3 4 5 6 7 2 345 67

A student graphed the linear equation y = 4, as shown above in figure (b). Explain her error.

How do we find the intercepts of the graph of an equation without having to graph the equation?

In Section 3.2, we discussed a method to graph y = 2x - 3. In Section 3.3, we discussed a method to graph 2x + 3y = 6. Briefly explain the steps involved in each method.

Simplify: 3 5 5 3 5 5 5 2x 

Simplify: 41 d 2 32 51 2 5 d 12 3

Translate: Six less than twice x

Is -5 a solution of 2(3x + 10) = 5x + 6?

Where will the line y = b intersect the line x = a?

Write an equation of the line that has an x-intercept of (4, 0) and a y-intercept of (0, 3).

What is the least number of intercepts a line can have? What is the greatest number a line can have?

On a rectangular coordinate system, draw a circle that has exactly two intercepts.

The _____ of a line is a measure of the lines steepness. It is the _____ of the vertical change to the horizontal change.

m = _______ horizontal change rise change in y.

The rate of _____ of a linear relationship can be found by finding the slope of the graph of the line and attaching the proper units.

______ lines do not intersect. _____lines intersect to form four right angles.

Which line graphed has a. a positive slope? b. a negative slope? c. zero slope? d. undefined slope? Line 3 Line 4 Line 2 Line 1 11 1 1 2 3 4 2 3 4 234

Consider each graph of a line and the slope triangle. What is the rise? What is the run? What is the slope of the line? a. y x 111 1 2 2 3 4 5 6 b. y x 11 1 1 2 3 4 5 2 3 234

For each graph, determine which line has the greater slope. a. y Line 1 Line b. y Line 1 Line 2 c. x y Line 1 L

Which two labeled points should be used to find the slope of the line? y x E D C 1 1 1 2 3 2 3 234 2 3 4

a. Find the slope of the line below using the points in black. b. Find the slope of the line using the points in green. c. Fill in the blank: When finding the slope of a line, the value will be obtained no matter which two points on the line are used. y x 111 1 2 3 4 2 3 4 23456

Evaluate each expression. a. 10 4 6 5 b. 1 1 2 (7) 10

Write each slope in a better way. a. m 0 6 b. m 8 0 m c. m 3 12 d. m 10 5 m

Fill in the blanks: _____ lines have a slope of 0. Vertical lines have _____ slope.

The grade of an incline is its slope expressed as a percent. Express the slope 2 5 as a grade.

Growth Rates. The graph shows how a childs height increased from ages 2 through 5. Fill in the correct units to find the rate of change in the childs height. Rate of change (40 31) (5 2) 2 210 30 32 34 36 38 40 42 44 3456 x y

Find the negative reciprocal of each number. a. 6 b. 7 8 c. 1

Fill in the blanks. a. Two different lines with the same slope are _____ . b. If the slopes of two lines are negative reciprocals, the lines are _____. c. The product of the slopes of perpendicular lines is .

a. What is the formula used to find the slope of a line passing through (x ) 1, y1) and (x2, y2 (x )? b. Fill in the blanks to state the slope formula in words: m equals y ____ two minus y ____ one _____ x sub ____ minus x sub ____ .

Explain the difference between y2 and y2.

Consider the points (7, 2) and (4, 1). If we let x1 7, then what is y2?

The symbol is used when graphing to indicate a _____ in the labeling of an axis.

Find the slope of each line. See Example 1. y x 111 1 2 3 4 2 3 4 234

Find the slope of each line. See Example 1. y x 111 1 2 3 4 2 3 4 234 2 3 4

Find the slope of each line. See Example 1. y x 111 1 2 3 4 2 3 4 234 2 3 4

Find the slope of each line. See Example 1. y x 111 1 2 3 4 5 2 3 234 2 3 4

Find the slope of each line. See Example 1. y x 111 1 2 2 3 4 5 6 234 2 3 4

Find the slope of each line. See Example 1. y x 111 1 2 3 4 2 3 4 234 2 3 4

Find the slope of each line. See Example 1. y x 111 1 2 3 4 5 6 2 234 2 3 4

Find the slope of each line. See Example 1. y x 111 1 2 3 4 2 3 4 234 2 3 4

Find the slope of each line. See Example 1. x 111 1 2 3 4 2 3 4 234 2 3 4

Find the slope of each line. See Example 1. x 111 1 2 3 4 2 3 4 234 2 3 4

Find the slope of each line. See Example 1. y x 111 1 2 2 3 4 5 6 2 2 3 4 5 6

Find the slope of each line. See Example 1. y x 111 1 2 3 4 5 6 2 2 2 3 4 5 6

Find the slope of the line passing through the given points. See Examples 2 and 3. (1, 3) and (2, 4)

Find the slope of the line passing through the given points. See Examples 2 and 3. (1, 3) and (2, 5)

Find the slope of the line passing through the given points. See Examples 2 and 3. (3, 4) and (2, 7)

Find the slope of the line passing through the given points. See Examples 2 and 3. (3, 6) and (5, 2)

Find the slope of the line passing through the given points. See Examples 2 and 3. (0, 0) and (4, 5)

Find the slope of the line passing through the given points. See Examples 2 and 3. (4, 3) and (7, 8)

Find the slope of the line passing through the given points. See Examples 2 and 3. (3, 5) and (5, 6) (6

Find the slope of the line passing through the given points. See Examples 2 and 3. (6, 2) and (3, 2)3

Find the slope of the line passing through the given points. See Examples 2 and 3. (2, 2) and (12, 8) (1,

Find the slope of the line passing through the given points. See Examples 2 and 3. (1, 2) and (10, 5) (3,

Find the slope of the line passing through the given points. See Examples 2 and 3. (5, 7) and (4, 7) (

Find the slope of the line passing through the given points. See Examples 2 and 3. (1, 12) and (6, 12) (2

Find the slope of the line passing through the given points. See Examples 2 and 3. 8, 4) and (8, 3) (2

Find the slope of the line passing through the given points. See Examples 2 and 3. (2, 8) and (2, 15) (5

Find the slope of the line passing through the given points. See Examples 2 and 3. (6, 0) and (0, 4) (0

Find the slope of the line passing through the given points. See Examples 2 and 3. (0, 9) and (6, 0)(

Find the slope of the line passing through the given points. See Examples 2 and 3. (2.5, 1.75) and (0.5, 7.75) (6,

Find the slope of the line passing through the given points. See Examples 2 and 3. (6.4, 7.2) and (8.8, 4.2)

Find the slope of the line passing through the given points. See Examples 2 and 3. (2.2, 18.6) and (1.7, 18.6)(

Find the slope of the line passing through the given points. See Examples 2 and 3. (4.6, 3.2) and (4.6, 4.8)

Find the slope of the line passing through the given points. See Examples 2 and 3. 1 2 4 7, 1 52 and 1 2 3 7, 6 5 1 2 4

Find the slope of the line passing through the given points. See Examples 2 and 3. 4 9, 1 82 and 5 9, 3 8 1 2 3

Find the slope of the line passing through the given points. See Examples 2 and 3. 1 2 3 4, 2 32 and 1 4 3, 1 62

Find the slope of the line passing through the given points. See Examples 2 and 3. 1 1 2, 3 42 and 111 16, 1 2 1 2 3

Determine the slope of the graph of the line that has the given table of solutions. See Examples 2 and 3. 1 2 (1, 2) 3 1 (3, 1) yx (x,

Determine the slope of the graph of the line that has the given table of solutions. See Examples 2 and 3. 6 0 2 (0, 2) 3 (3, 6) yx (x

Determine the slope of the graph of the line that has the given table of solutions. See Examples 2 and 3. 3 6 (3, 6) 6 (0, 6) yx (x,

Determine the slope of the graph of the line that has the given table of solutions. See Examples 2 and 3. 0) 5 (4, 5) yx (x

Find the slope of each line. See Examples 4 and 5. y = -11

Find the slope of each line. See Examples 4 and 5. y = -2

Find the slope of each line. See Examples 4 and 5. y = 0

Find the slope of each line. See Examples 4 and 5. x = 0

Find the slope of each line. See Examples 4 and 5. x = 6

Find the slope of each line. See Examples 4 and 5. x = 4

Find the slope of each line. See Examples 4 and 5. x = -10

Find the slope of each line. See Examples 4 and 5. y = 8

Find the slope of each line. See Examples 4 and 5. y - 9 = 0

Find the slope of each line. See Examples 4 and 5. x + 14 = 0

Find the slope of each line. See Examples 4 and 5. 3x = - 12

Find the slope of each line. See Examples 4 and 5. 2y + 2 = -6

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. (5, 3) and (1, 4) (3, 4) and (1, 5) (8,

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. (2, 4) and (1, 1) (8, 0) and (11, 5)

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. (4, 2) and (2, 3) (2, (7, 1) and (8, 7)

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. (2, 4) and (6, 7) (6, 4) and (5, 12)

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. (2, 2) and (4, 3) (3, 4) and (1, 9) (5,

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. (1, 3) and (2, 4) (5, 2) and (8, 5)

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. (1, 8) and (6, 8) (1 (3, 3) and (3, 7)

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. (11, 0) and (11, 5) (14, 6) and (25, 6)

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. (6, 4) and (2, 5) (2, 3) and (2, 4) (8,

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. (3, 1) and (3, 2) (8, 2) and (9, 8)

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. 4, 2) and (5, 3) (5, 3) and (2, 9) (

Determine whether the lines through each pair of points are parallel, perpendicular, or neither. See Example 8. (8, 3) and (8, 8) (11, 3) and (22, 3)

Find the slope of a line perpendicular to the line passing through the given two points. See Example 9. (0, 0) and (5, -9)

Find the slope of a line perpendicular to the line passing through the given two points. See Example 9. (0, 0) and (5, 12)

Find the slope of a line perpendicular to the line passing through the given two points. See Example 9. (-1, 7) and (1, 10)

Find the slope of a line perpendicular to the line passing through the given two points. See Example 9. (-7, 6) and (0, 4)

Find the slope of a line perpendicular to the line passing through the given two points. See Example 9. 12, , 22 1 2 2 and 11, 3 22 (1

Find the slope of a line perpendicular to the line passing through the given two points. See Example 9. 3, 12 and 1 4 3 12, , 2 1

Find the slope of a line perpendicular to the line passing through the given two points. See Example 9. (-1, 2) and (-3, 6)

Find the slope of a line perpendicular to the line passing through the given two points. See Example 9. (5, -4) and (-1, -7)

Pools. Find the slope of the bottom of the swimming pool as it drops off from the shallow end to the deep end. 5' 15' 10' 9' 3' Deep end Sh

Drainage. Find the slope of the concrete patio slab using the 1-foot ruler, level, and 10-foot-long board shown in the illustration. (Hint: 10 feet 120 in.) 1 2 3 4 5 6 7 8 9 10 11 Patio slab

Grade of a Road. Refer to the illustration below. Find the slope of the decline and use that information to find the grade of the road. 1 mi (5,280 ft) ?

Streets. One of the steepest streets in the United States is Eldred Street in Highland Park, California (near Los Angeles). It rises approximately 220 feet over a horizontal distance of 665 feet. What is the grade of the street?

Treadmills. Find the slope of the jogging surface of the treadmill for a height setting of 6 inches. Then express the incline as a percent. Height setting 50 in.

Architecture. Locate the coordinates of the peak of the roof if it is to have a pitch of 2 5 and the roof line is to pass through the two given points in black. y 5 5 10 10 15 20

Carpentry. Find the pitch of each roof. Front Side

Doll Houses. Find so that the pitch of the roof of the doll house is 4 3. x 2 ft 6 in.

Irrigation. The graph on the next page shows the number of gallons of water remaining in a reservoir as water is used from it to irrigate a field. Find the rate of change in the number of gallons of water in the reservoir. 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 23456 Hours irrigating Gallons of water in reservoi

Commercial Jets. Examine the graph and consider trips of more than 7,000 miles by a Boeing 777. Use a rate of change to estimate how the maximum payload decreases as the distance traveled increases. 20,000 0 40,000 60,000 80,000 100,000 120,000 140,000 5,000 Distance (mi) Maximum payload (lb)

Milk Production. The following graph approximates the amount of milk produced per cow in the United States for the years 19962009. Find the rate of change. 21,000 Pounds '96 '98 '00 Year '02 '04 '06 '08 '10 Source: USDA; Agricultural and Applied Economics, UW Madison 16, 433 20, 580

Wal-Mart. The graph in the next column approximates the sales revenue of Wal-Mart for the years 19912009. Find the rate of change in revenue for the years a. 19911998 b. 19982009500 $ billions Wal-Mart Net Sales 19912009 '92'90 '94 '96 Year '98 '00 '02 $405 $35 300 $119 '04 '06 '08 '10

Dental Assistant In 2000, there were approximately 6,600 students enrolled in dental assisting programs in the U.S. By 2008, that number had steadily increased to about 9,200 students. Find the rate of change in the number of students studying to be dental assistants from 2000 to 2008. (Source: American Dental Education Association)

Firefighting. When flames are tilted due to effects of wind, firefighters measure what is called the slope percent of the flames. Calculate the slope percent of the flame shown below by expressing its slope as a percent. (Source math.fire.org) 12 ft 9

Explain why the slope of a vertical line is undefined.

How do we distinguish between a line with positive slope and a line with negative slope?

Explain the error in the following solution: Find the slope of the line that passes through (6, 4) and (3, 1). m 1 4 6 3 3 3 1 (6, 4)

Explain the difference between a rate of change that is positive and one that is negative. Give an example of each.

Halloween Candy. A candy maker wants to make a 60-pound mixture of two candies to sell for $2 per pound. If black licorice bits sell for $1.90 per pound and orange gumdrops sell for $2.20 per pound, how many pounds of each should be used?

Medications. A doctor prescribes an ointment that is 2% hydrocortisone. A pharmacist has 1% and 5% concentrations in stock. How many ounces of each should the pharmacist use to make a 1-ounce tube?

Use the concept of slope to determine whether A(-50, -10), B(20, 0), and C(34, 2) all lie on the same straight line.

A line having slope 2 3 passes through the point (10, 12). What is the y-coordinate of another point on the line whose x-coordinate is 16?

Subscripts are used in other disciplines besides mathematics. In what disciplines are the following symbols used? a. H2O and CO2 b. C7 and G7 c. B6 and B12

Evaluate for , 2a a2 2, a3 3 and . a4

The equation y = mx + b is called the _____ form of the equation of a line.

The graph of the linear equation y = mx + b has ____ (0, b) and _____ m .

Determine whether each equation is in slopeintercept form. a. 7x 4y 2 b. 5y 2x 3 c. y 6x  1 x d. x 4y 87

a. Fill in the blank: To write a linear equation in two variables in slopeintercept form, solve the equation for. b. Solve 4x  y 9 for y.

Simplify the right side of each equation. a. y 4x 2  16 2 b. y 15x 3  9 3 y c. y 2x 6 6 6 y d. y 9x 5 20 5 y 2x

Find the slope and -intercept of each line graphed below. Then use that information to write an equation for that line. y 111 1 2 2 3 4 5 6 2 2 3 4 5 6 x y 111 1 2 3 4 5

Complete the solution by solving the equation for y. Then find the slope and the y-intercept of its graph. 2x  5y 15 2x  5y 2x  15 y x  5y 2x  15 2x  The slope is and the -intercept is .

What is the slopeintercept form of the equation of a line?

Fill in the blanks: 3 2 3 2 y

Determine whether each statement is true or false. a. x 6 1 6 x b. 5 3 x 5x 3

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 4x  2 y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 7x  3

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 5x 8 y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 4x 2 y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 25x 9 y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 6x 1 y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 11 x y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 12 4x y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 1 2 x  6 y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 4 5 y x 9 1

Find the slope and the y-intercept of the line with the given equation. See Example 1. y x 4 1 2 y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y x 15 3 4 y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 5x y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 14x

Find the slope and the y-intercept of the line with the given equation. See Example 1. y x y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y x y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 2 y

Find the slope and the y-intercept of the line with the given equation. See Example 1. y 30

Find the slope and the y-intercept of the line with the given equation. See Example 1. 5y 2 0 3y

Find the slope and the y-intercept of the line with the given equation. See Example 1. 3y 13 0 y

Find the slope and the y-intercept of the line with the given equation. See Example 1. x  y 8 x

Find the slope and the y-intercept of the line with the given equation. See Example 1. x y 30 5y

Find the slope and the y-intercept of the line with the given equation. See Example 1. 6y x 6 2y

Find the slope and the y-intercept of the line with the given equation. See Example 1. 2y x  20

Find the slope and the y-intercept of the line with the given equation. See Example 1. 4y 6x 4 6y

Find the slope and the y-intercept of the line with the given equation. See Example 1. 6y 8x  6 6y

Find the slope and the y-intercept of the line with the given equation. See Example 1. 2x  3y 6 4

Find the slope and the y-intercept of the line with the given equation. See Example 1. 4x  5y 25

Find the slope and the y-intercept of the line with the given equation. See Example 1. 3x 5y 15 x

Find the slope and the y-intercept of the line with the given equation. See Example 1. x 6y 6 2

Find the slope and the y-intercept of the line with the given equation. See Example 1. 6x  6y 11 4x

Find the slope and the y-intercept of the line with the given equation. See Example 1. 4x  4y 9 3x

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope 5, y-intercept (0, -3)

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope -2, y-intercept (0, 1)

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope -3, y-intercept (0, 6)

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope 4, y-intercept (0, 1)

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope 1 4, y-intercept (0, 2)

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope 1 3, y-intercept (0, 5)

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope 8 3, y-intercept (0, 5)

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope 7 6, y-intercept (0, 2)

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope 6 5, y-intercept (0, 0)

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope 5 4, y-intercept (0, 0)

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope 2, y-intercept a0, y b 1 2 y b

Write an equation of the line with the given slope and y-intercept and graph it. See Example 2. Slope 3, y-intercept a0, 1 2 a0, y b 1

Write an equation for each line shown below. See Example 3. y 111 1 2 3 4 2 3 4 234 2 3 4

Write an equation for each line shown below. See Example 3. y 111 1 2 3 4 2 3 4 234 2 3 4

Write an equation for each line shown below. See Example 3. y 111 1 2 3 4 2 3 4 234 2 3 4

Write an equation for each line shown below. See Example 3. y 111 1 2 3 4 2 3 4 234 2 3 4

Write an equation for each line shown below. See Example 3. 111 1 2 3 4 2 3 4 23 2 3 4 5

Write an equation for each line shown below. See Example 3. 111 1 2 3 4 2 3 4 23 2 3 4 5

Write an equation for each line shown below. See Example 3. y 111 1 2 3 4 2 3 4 234 2 3 4

Write an equation for each line shown below. See Example 3. y 111 1 2 3 4 2 3 4 2 2 3 4 5 6

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. y 3x  3 y

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. y 3x  5 x

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. y 1 2 x  2

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. y x 3 y

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. 3x y

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. y 4x y

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. 4x  y 4 2x

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. 2x  y 6 y

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. 3x  4y 16 2

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. 2x  3y 9

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. 10x 5y 5 4x

Find the slope and the y-intercept of the graph of each equation and graph it. See Examples 4 and 5. 4x 2y 6 3

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. y 6x  8 y y 6x

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. y 9x 3 10 y 9x y

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. y x y y x y

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. y 3x y 4x

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. y 1 2 x 4 5 y y 0.5x  3 x

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. y 3x 15 1 y 1 3 x  4 y

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. y 2x 9 x  2x y 9 4x

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. y 3 4 x  1 y 4x 3y 15 y

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. 3x 5y 10 2y 5x 1 3y 2x

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. 2y 2 x 2x 2x 3 4y 3

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. x y 12 y 2x  2y 23 3y

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. y 3x  1 5x 3y x 5 x

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. x 9 x y 8 2

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. x  4y 10 2 2y  16 8x x

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. 4x  3y 12 5x 8x  6y 54 1

For each pair of equations, determine whether their graphs are parallel, perpendicular, or neither. See Example 6. 5x  2y 8 y 15x  6y 48 4

Production Costs. A television production company charges a basic fee of $5,000 and then $2,000 an hour when filming a commercial. a. Write a linear equation that describes the relationship between the total production costs c and the hours h of filming. b. Use your answer to part a to find the production costs if a commercial required 8 hours of filming.

College Fees. Each semester, students enrolling at a community college must pay tuition costs of $20 per unit as well as a $40 student services fee. a. Write a linear equation that gives the total fees to be paid by a student enrolling at the college and taking x units. b. Use your answer to part a to find the enrollment cost for a student taking 12 units.

Chemistry. A portion of a students chemistry lab manual is shown on the right. Use the information to write a linear equation relating the temperature F in degrees Fahrenheit of the compound to the time (in minutes) elapsed during the lab procedure. Chem. Lab #1 Aug. 13 Step 1: Removed compound from freezer @ 10F. Step 2: Used heating unit to raise temperature of compound 5 F every minute.

Rentals. Use the information in the newspaper advertisement to write a linear equation that gives the amount of income A (in dollars) the apartment owner will receive when the unit is rented for m months.

Employment Services. A policy statement of LIZCO, Inc., is shown below. Suppose a secretary had to pay an employment service $500 to get placed in a new job at LIZCO. Write a linear equation that tells the secretary the actual cost c of the employment service to her months after being hired. Policy no. 23452A new hire will be reimbursed by LIZCO for any employment service fees paid by the employee at the rate of $20 per month.

Printing Presses. Every three minutes, 100 feet of paper is used off of an 8,000 foot-roll to print the pages of a magazine. Write a linear equation that relates the number of feet of paper that remain on the roll and the number of minutes the printing press has been operating.

Sewing Costs. A tailor charges a basic fee of $20 plus $5 per letter to sew an athletes name on the back of a jacket. Write a linear equation that will find the cost to have a name containing letters sewn on the back of a jacket.

Salad Bars. For lunch, a delicatessen offers a Salad and Soda special where customers serve themselves at a wellstocked salad bar. The cost is $2.00 for the drink and 42 an ounce for the salad. Write a linear equation that will find the cost of a Salad and Soda lunch when a salad weighing ounces is purchased.

iPads. When a student purchased an Apple iPad with Wi-Fi + 3G for $629.99, he also enrolled in a 250 MB data plan that cost $14.95 per month. a. Write a linear equation that gives the cost for him to purchase and use the iPad for m months. b. Use your answer to part a to find the cost to purchase and use the iPad for 2 years.

Online Games. A new Playstation 3 costs $310.50 and membership in an online videogame multiplayer network cost $18.49 per month. a. Write a linear equation that gives the cost for someone to buy the machine and belong to the online network for m months. b. Use your answer to part a to find the cost to buy the machine and belong to the network for 3 years.

Navigation. The graph below shows the recommended speed at which a ship should proceed into head waves of various heights. a. What information does the -intercept of the line give? b. What is the rate of change in the recommended speed of the ship as the wave height increases? c. Write an equation of the line. y 2 4 2 6 8 10 12 14 16 18 468 Wave height (ft) Ship speed (knots) 10 12 14 16 18 20 22 24

Debt. The graph below estimates the amount of credit card debt per U.S. household for the years 19902010. a. What information does the d-intercept of the line give? b. What was the rate of change in the amount of debt per household? c. Write an equation of the line, where d is the approximate credit card debt and t is the number of years since 1990. Source: mybudget 360.com t 0 10 15 20 25 5 Years since 1990 Credit card debt per U.S. household ($) 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,

Why is y = mx + b called the slopeintercept form of the equation of a line?

On a quiz, a student was asked to find the slope of the graph of y = 2x + 3 m . She answered: m = . Her instructor marked it wrong. Explain why the answer is incorrect.x

Cable TV. A 186-foot television cable is to be cut into four pieces. Find the length of each piece if each successive piece is 3 feet longer than the previous one.

Investments. Joni received $25,000 as part of a settlement in a class action lawsuit. She invested some money at 10% and the rest at a 9% simple interest rate. If her total annual income from these two investments was $2,430, how much did she invest at each rate?

If the graph of y = mx + b passes through quadrants I, II, and IV, what can be known about the constants m and b?

Which of the following equations has the steeper graph, 103x 200y 400 or 17x 33y 66? bm

y - y1 = m(x - x1)24 is called the ______ form of the equation of a line. In words, we read this as y minus y ______ one equals m ______ the quantity of x ________ x sub ______ .

y = mx + b is called the ______ form of the equation of a line.

Determine in what form each equation is written. a. y - 4 = 2(x - 5) b. y = 2x + 15

What point does the graph of each equation pass through, and what is the lines slope? a. y - 2 = 6(x - 7) b. y + 3 = -8 (x + 1)

Refer to the following graph of a line. a. What highlighted point does the line pass through? b. What is the slope of the line? c. Write an equation of the line in pointslope form. y 111 1 2 3 4 2 3 4 234 2 3 4

On a quiz, a student was asked to write the equation of a line with slope 4 that passes through (-1, 3). Explain how the student can check her answer, y = 4x + 7.

Suppose you are asked to write an equation of the line in the scatter diagram below. What two points would you use to write the pointslope equation? y x 65 70 75 80 Weight (lb) Height (in.) 140 160 180 200 220 240

In each case, a linear relationship between two quantities is described. If the relationship were graphed, what would be the slope of the line? a. The sales of new cars increased by 15 every 2 months. b. There were 35 fewer robberies for each dozen police officers added to the force. c. One acre of forest is being destroyed every 30 seconds.

Complete the solution. Find an equation of the line with slope that passes through the point . Write the answer in slopeintercept form. y y1 m(x x1) (1 y 2[x ( )] y y 2x  y 5 2x y 5 2[

What is the pointslope form of the equation of a line?

Consider the steps below and then fill in the blanks: y 3 2(x  1) y y 3 2x  2 y y 2x  5 The original equation was in ______ form. After solving for , we obtain an equation in ______ form.

Fill in the blanks: The equation of a horizontal line has the form = b and the equation of a vertical line has the form a.

Use the pointslope form to write an equation of the line with the given slope and point. Leave the equation in that form. See Example 1. Slope 3, passes through (2, 1)

Use the pointslope form to write an equation of the line with the given slope and point. Leave the equation in that form. See Example 1. Slope 2, passes through (4, 3)

Use the pointslope form to write an equation of the line with the given slope and point. Leave the equation in that form. See Example 1. Slope 4 5 , passes through (5, 1)

Use the pointslope form to write an equation of the line with the given slope and point. Leave the equation in that form. See Example 1. Slope 7 8 , passes through (2, 9)

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope 2, passes through (3, 5)

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope 8, passes through (2, 6)

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope -5, passes through (-9, 8)

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope -4, passes through (-2, 10)

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope -3, passes through the origin

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope -1, passes through the origin

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope 1 5 , passes through (10, 1)

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope 1 4, passes through (8, 1)

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope 4 3, 6 4 yx

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope 3 2 2 1 yx

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope 11 6 , passes through (2, 6)

Use the pointslope form to find an equation of the line with the given slope and point. Then write the equation in slopeintercept form. See Example 1. Slope5 4, passes through (2, 0)

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. Passes through (1, 7) and (-2, 1)

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. Passes through (-2, 2) and (2, -8)

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. 3 2 0 4 yx

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. 1 2 1 4 yx 33

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. Passes through (5, 5) and (7, 5)

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. Passes through (-2, 1) and (-2, 15)

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. Passes through (5, 1) and (-5, 0)

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. Passes through a (-3, 0) and (3, 1)

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. Passes through (-8, 2) and (-8, 17)

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. Passes through 2 3, 22 and (0, 2)

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. Passes through 2 3, 1 3 and (0, 0)

Find an equation of the line that passes through the two given points. Write the equation in slopeintercept form, if possible. See Example 2. Passes through 1 2, 3 4 and (0, 0)

Write an equation of each line. See Example 3. Vertical, passes through (4, 5)

Write an equation of each line. See Example 3. Vertical, passes through (-2, -5)

Write an equation of each line. See Example 3. Horizontal, passes through (4, 5)

Write an equation of each line. See Example 3. Horizontal, passes through (-2, -5)

Graph the line that passes through the given point and has the given slope. See Example 4. (1, 2) , m 4

Graph the line that passes through the given point and has the given slope. See Example 4. (4, 1) 3 m 3

Graph the line that passes through the given point and has the given slope. See Example 4. (5, 3), m m 3 4

Graph the line that passes through the given point and has the given slope. See Example 4. (2, 4), m 2 3

Graph the line that passes through the given point and has the given slope. See Example 4. (2, 3) slope 2

Graph the line that passes through the given point and has the given slope. See Example 4. (3, 3) slope 4

Graph the line that passes through the given point and has the given slope. See Example 4. (4, 3) slope 5 7 8

Graph the line that passes through the given point and has the given slope. See Example 4. (4, 2) slope 1 5

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Passes through (5, 0) and (-11, -4)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Passes through (7, -3) and (-5, 1)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Horizontal, passes through (-8, 12)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Horizontal, passes through (9, -32)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 1 4, y-intercept 0, 7 8

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 9 5 y-intercept a0, 11 3 b 9

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 2 3, passes through (3, 0)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 2 5, passes through (15, 0)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 8, passes through (2, 20)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 6, passes through (1, -2)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Vertical, passes through (-3, 7)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Vertical, passes through (12, -23)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 7 and y-intercept (0, -11)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 3 and y-intercept (0, 4)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Passes through (-2, -1) and (-1, -5)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Passes through (-3, 6) and (-1, -4)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. x-intercept (7, 0) and -intercept (0, -2)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. x-intercept (-3, 0) and y-intercept (0, 7)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 1 10, passes through the origin

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 9 8 , passes through the origin

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Undefined slope, passes through a1 8 , 12b 9

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Undefined slope, passes through a 2 5 , 5 6 b a

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 1.7, y-intercept (0, -2.8)

Use either the slopeintercept form (from Section 3.5) or the pointslope form (from Section 3.6) to find an equation of each line. Write each result in slopeintercept form, if possible. Slope 9.5, y-intercept (0, -14.3)

Anatomy. There is a linear relationship between a womans height and the length of her radius bone. It can be stated this way: Height increases by 3.9 inches for each 1-inch increase in the length of the radius. Suppose a 64-inch-tall woman has a 9-inch-long radius bone. Use this information to find a linear equation that relates height to the length of the radius. Write the equation in slopeintercept form. h r

Automation. An automated production line uses distilled water at a rate of 300 gallons every 2 hours to make shampoo. After the line had run for 7 hours, planners noted that 2,500 gallons of distilled water remained in the storage tank. Find a linear equation relating the time in hours since the production line began and the number of gallons of distilled water in the storage tank. Write the equation in slopeintercept form.

Pole Vaulting. Find the equations of the lines that describe the positions of the pole for parts 1, 3, and 4 of the jump. Write the equations in slopeintercept form, if possible.

Freeway Design. The graph below shows the route of a proposed freeway. a. Give the coordinates of the points where the proposed Freeway 133 will join Interstate 25 and Highway 40. b. Find an equation of the line that describes the route of the proposed freeway. Write the equation in slopeintercept form. y Proposed freeway 133 25 1 1 1 1 2

Toxic Cleanup. Three months after cleanup began at a dump site, 800 cubic yards of toxic waste had yet to be removed. Two months later, that number had been lowered to 720 cubic yards. a. Find an equation that describes the linear relationship between the length of time (in months) the cleanup crew has been working and the number of cubic yards of toxic waste remaining. Write the equation in slopeintercept form. b. Use your answer to part (a) to predict the number of cubic yards of waste that will still be on the site one year after the cleanup project began.

Depreciation. To lower its corporate income tax, accountants of a company depreciated a word processing system over several years using a linear model, as shown in the worksheet. a. Find a linear equation relating the years since the system was purchased, , and its value, , in dollars. Write the equation in slopeintercept form. b. Find the purchase price of the system. Tax Worksheet Method of depreciation: Linear Property Word processing system $60,000 $30,000 Value 2 4 Years after purchase

Trampolines. There is a linear relationship between the length of the protective pad that wraps around a trampoline and the radius of the trampoline. Use the data in the table to find an equation that gives the length of pad needed for any trampoline with radius . Write the equation in slopeintercept form. Use units of feet for both l and r. Protective pad radius Radius Pad length 3 ft 19 ft 7 ft 44 ft

Raising a Family. In the report Expenditures on Children by Families, the U.S. Department of Agriculture projected the yearly child-rearing expenditures on children from birth through age 17. For a child born in 2010 to a two-parent middle-income family, the report estimated annual expenditures of $10,808 when the child is 6 years old, and $14,570 when the child is 15 years old. a. Write two ordered pairs of the form (child's age, annual expenditure). b. Assume the relationship between the child's age a and the annual expenditures E is linear. Use your answers to part (a) to write an equation in slopeintercept form that models this relationship. c. What are the projected child-rearing expenses when the child is 17 years old?

Got Milk? The scatter diagram shows the amount of milk that an average American drank in one year for the years 19802008. A straight line can be used to model the data. a. Use the two highlighted points on the line to find its equation. Write the equation in slopeintercept form. b. Use your answer to part (a) to predict the amount of milk that an average American will drink in 2020.30 Years after 1980 U.S. Milk Consumption (per capita) Gallons of milk 5 10 15 20 25 28 (2008)

Engine Output. The horsepower produced by an automobile engine was recorded for various engine speeds in the range of 2,400 to 4,800 revolutions per minute (rpm). The data were recorded on the following scatter diagram. Find an equation of the line that models the relationship between engine speed and horsepower . Write the equation in slopeintercept form. s h 2,400 2,800 3,200 3,600 4,000 4,400 4,800 5,200 150 Engine speed (rpm) Horsepo wer (hp) 170 190 210 230 250 270 290 310 330 350

Why is y y1 m(x x1)3 called the pointslope form of the equation of a line?

If we know two points that a line passes through, we can write its equation. Explain how this is done.

Explain the steps involved in writing y 6 4(x 1) y in slopeintercept form

Think of the points on the graph of the horizontal line y = 4. What do the points have in common? How do they differ?

Frames. The length of a rectangular picture is 5 inches greater than twice the width. If the perimeter is 112 inches, find the dimensions of the frame.

Speed of an Airplane. Two planes are 6,000 miles apart, and their speeds differ by 200 mph. They travel toward each other and meet in 5 hours. Find the speed of the slower plane.

Find an equation of the line that passes through and is parallel to the line y 4x 7. Write the equation in slopeintercept form.

Find an equation of the line that passes through and is perpendicular to the liney 3x 12. Write the equation in slopeintercept form.

2x y 4 4 is a linear _____ in two variables.

An ordered pair (x, y) is a ______ of a linear inequality in two variables if a true statement results when the values of the variables are substituted into the inequality.

(7, 2) is a solution of x - y > 1. We say that (7, 2) _____ the inequality.

In the graph, the line 2x - y = 4 is the _____ line. y x 2x y = 4 2x y 4 111 1 2 3 4 2 3 4 234

In the graph, the line 2x - y = 4 divides the coordinate plane into two ______. y x 2x y = 4 2x y 4 111 1 2 3 4 2 3 4 234

When graphing a linear inequality, we determine which half-plane to shade by substituting the coordinates of a test _____ into the inequality.

Determine whether (3, 5) 5x is a solution of 5x 3y  0.

Determine whether (3, 1) x is a solution of (3, 1) x  4y  1. (3

Fill in the blanks: A ____ line indicates that points on the boundary are not solutions and a _____ line indicates that points on the boundary are solutions.

The boundary for the graph of a linear inequality is shown. Why cant the origin be used as a test point to decide which side to shade? x 111 1 2 3 4 2 3 4 234 2 3 4

If a false statement results when the coordinates of a test point are substituted into a linear inequality, which half-plane should be shaded to represent the solution of the inequality?

A linear inequality has been graphed. Determine whether each point satisfies the inequality. a. b. c. d. (3, 4) (2, 3) (2, 1) (1, 3) y y x 111 1 2 3 4 2 3 4 234 2 3 4

A linear inequality has been graphed. Determine whether each point satisfies the inequality. a. b. c. d. (3, 4) (4, 2) (2, 4) (2, 1) y x y x 111 1 2 3 4 2 3 4 234 2 3 4

To graph linear inequalities, we must be able to graph boundary lines. Complete the table of solutions for each given boundary line. a. 5x 3y  15 b. y  3x 2 0 0 1 yx (x, y) 0 2 1 yx (x, y) NO

Write the meaning of each symbol in words. a.  b. c. d.  ?

a. When graphing linear inequalities, which inequality symbols are associated with a dashed boundary line? b. When graphing linear inequalities, which inequality symbols are associated with a solid boundary line?

Fill in the blanks: The inequality 4x  2y 9 means 4x  2y 9 or 4x  2y 9

Fill in the blanks: The inequality x  8y  14 means x  8y 1 or x  8y 1. x

Determine whether each ordered pair is a solution of the given inequality. See Example 1. 2x  y  6; (3, 2)

Determine whether each ordered pair is a solution of the given inequality. See Example 1. 4x 2y  6; (2, 1) 25

Determine whether each ordered pair is a solution of the given inequality. See Example 1. 5x 8y  8; (8, 4) x 

Determine whether each ordered pair is a solution of the given inequality. See Example 1. x  3y  14; (3, 8)

Determine whether each ordered pair is a solution of the given inequality. See Example 1. 4x y 0; a , 1b 1 2 , 1b 5x

Determine whether each ordered pair is a solution of the given inequality. See Example 1. x y 2; a 1 3 4x y 0; a , 1b 1

Determine whether each ordered pair is a solution of the given inequality. See Example 1. 5x  2y  4; (0.8, 0.6) 9

Determine whether each ordered pair is a solution of the given inequality. See Example 1. 6x 2y  7; (0.2, 1.5) 5x

Complete the graph by shading the correct side of the boundary. See Example 2. x y  2 x 4 2 3 4 234 2 3 4

Complete the graph by shading the correct side of the boundary. See Example 2. x y  3 y x 111 1 2 3 4 2 3 4 234 2 3 4

Complete the graph by shading the correct side of the boundary. See Example 2. y  2x 4 y y x 111 1 2 3 4 2 3 4 234 2 3 4

Complete the graph by shading the correct side of the boundary. See Example 2. y x  1 y x 111 1 2 3 4 2 3 4 234 2 3 4

Complete the graph by shading the correct side of the boundary. See Example 2. x 2y  4 3 y x 111 1 2 3 4 2 3 4 23 2 54

Complete the graph by shading the correct side of the boundary. See Example 2. 3x  2y  12 y x 111 1 2 3 4 5 6 7

Complete the graph by shading the correct side of the boundary. See Example 2. y 4x y x 11 1 2 3 4 3 4 234 2 3 4

Complete the graph by shading the correct side of the boundary. See Example 2. y  2x  0 y x 11 2 3 4 3 4 1 2 234 2 3 4

Graph each inequality. See Examples 2 and 3. x  y  3

Graph each inequality. See Examples 2 and 3. x  y  2

Graph each inequality. See Examples 2 and 3. 3x 4y  12 5

Graph each inequality. See Examples 2 and 3. 5x  4y  20

Graph each inequality. See Examples 2 and 3. 2x  3y 12 3x

Graph each inequality. See Examples 2 and 3. 3x 2y  6 3

Graph each inequality. See Examples 2 and 3. y  2x 1 y

Graph each inequality. See Examples 2 and 3. y  x  1

Graph each inequality. See Examples 2 and 3. y  3x  2

Graph each inequality. See Examples 2 and 3. y  2x  5

Graph each inequality. See Examples 2 and 3. y  1 3 2 x  1 enc

Graph each inequality. See Examples 2 and 3. y  x 3 y  1 3

Graph each inequality. See Examples 2 and 3. x 2y  4 4x

Graph each inequality. See Examples 2 and 3. 4x  y  4

Graph each inequality. See Examples 2 and 3. 2y x  8 y

Graph each inequality. See Examples 2 and 3. y  9x  3

Graph each inequality. See Examples 2 and 3. 7x 2y  21 3x

Graph each inequality. See Examples 2 and 3. 3x 3y  10 2

Graph each inequality. See Examples 2 and 3. 2x 3y  4 4

Graph each inequality. See Examples 2 and 3. 4x  3y  6

Graph each inequality. See Example 4. y  2x

Graph each inequality. See Example 4. y  3x

Graph each inequality. See Example 4. y  y  x x 2

Graph each inequality. See Example 4.  x

Graph each inequality. See Example 4. y  x  0

Graph each inequality. See Example 4. y x  0

Graph each inequality. See Example 4. 5x  3y  0

Graph each inequality. See Example 4. 2x  5y  0

Graph each inequality. See Example 5. x  2

Graph each inequality. See Example 5. y  3

Graph each inequality. See Example 5. y 1 x

Graph each inequality. See Example 5. x  4

Graph each inequality. See Example 5. y  2.5  0

Graph each inequality. See Example 5. x 1.5 0 y

Graph each inequality. See Example 5. x 0 y

Graph each inequality. See Example 5. y  0

Graph the given inequality in part a. Then use your answer to part a to help you quickly graph the associated inequality in part b. (Hint: If you spot the relationship between the inequalities, the graph in part b can be completed without having to use the test-point method.) a. 5x 3y  15 5x b. 5x 3y  15x

Graph the given inequality in part a. Then use your answer to part a to help you quickly graph the associated inequality in part b. (Hint: If you spot the relationship between the inequalities, the graph in part b can be completed without having to use the test-point method.) a. y  x  2 2 3 x  2 b. y 2 3 y  x  2 2

Graph the given inequality in part a. Then use your answer to part a to help you quickly graph the associated inequality in part b. (Hint: If you spot the relationship between the inequalities, the graph in part b can be completed without having to use the test-point method.) a. y  2x  0 b. y  2x  0

Graph the given inequality in part a. Then use your answer to part a to help you quickly graph the associated inequality in part b. (Hint: If you spot the relationship between the inequalities, the graph in part b can be completed without having to use the test-point method.) a. y x 1 4 x b. y  1 4 y x

Deliveries. To decide the number of pallets and the number y of barrels that a truck can hold, a driver refers to the graph below. Can a truck make a delivery of 4 pallets and 10 barrels in one trip? 1 2 3 45 67 5 10 15 20 25 30 T

Zoos. To determine the allowable number of juvenile chimpanzees and adult chimpanzees that can live in an enclosure, a zookeeper refers to the graph. Can 6 juvenile and 4 adult chimps be kept in the enclosure? y x 1 1 2 3 4 5 6 7 8 23456 Number of juvenile chimps Number of adult chimps 7 8 9 101112

Dental Assistant A dentist's office schedules 1-hour long appointments for adults and -hour long appointments for children. The appointment times do not overlap. Let c represent the number of appointments scheduled for children and a represent the number of appointments scheduled for adults. The graph of shows the possible ways the time for seeing patients can be scheduled so that it does not exceed 9 hours per day. Graph the inequality. Label the horizontal axis c and the vertical axis a. Then find three possible combinations of children/adult appointments.

Rolling Dice. The points on the graph represent all of the possible outcomes when two fair dice are rolled a single time. For example, , shown in red, represents a 5 on the first die and a 2 on the second. Which of the following sentences best describes the outcomes that lie in the shaded area? (i) Their sum is at most 6. (ii) Their sum exceeds 6. (iii) Their sum does not exceed 6. (iv) Their sum is at least 6. 1 2 3 4 Outcome on 2nd die 1st die 2nd die

Production Planning. It costs a bakery $3 to make a cake and $4 to make a pie. If represents the number of cakes made, and represents the number of pies made, the graph of 3x  4y 120 shows the possible combinations of cakes and pies that can be produced so that costs do not exceed $120 per day. Graph the inequality. Then find three possible combinations of cakes and pies that can be made so that the daily costs are not exceeded.

Hiring Babysitters. Mrs. Cansino has a choice of two babysitters. Sitter 1 charges $6 per hour, and Sitter 2 charges $7 per hour. If represents the number of hours she uses Sitter 1 and represents the number of hours she uses Sitter 2, the graph of 6x  7y 42 shows the possible ways she can hire the sitters and not spend more than $42 per week. Graph the inequality. Then find three possible ways she can hire the babysitters so that her weekly budget for babysitting is not exceeded.

Inventories. A clothing store advertises that it maintains an inventory of at least $4,400 worth of mens jackets at all times. At the store, leather jackets cost $100 and nylon jackets cost $88. If represents the number of leather jackets in stock and represents the number of nylon jackets in stock, the graph of 100x  88y  4,400 shows the possible ways the jackets can be stocked. Graph the inequality. Then find three possible combinations of leather and nylon jackets so that the store lives up to its advertising claim.

Making Sporting Goods. A sporting goods manufacturer allocates at least 2,400 units of production time per day to make baseballs and footballs. It takes 20 units of time to make a baseball and 30 units of time to make a football. If represents the number of baseballs made and represents the number of footballs made, the graph of 20x  30y  2,400 shows the possible ways to schedule the production time. Graph the inequality. Then find three possible combinations of production time for the company to make baseballs and footballs.

Explain how to decide which side of the boundary line to shade when graphing a linear inequality in two variables.

Why is the origin usually a good test point to choose when graphing a linear inequality?

Why is (0, 0) not an acceptable choice for a test point when graphing a linear inequality whose boundary passes through the origin?

Explain the difference between the graph of the solution set of x + 1 > 8, an inequality in one variable, and the graph of x + y > 8, an inequality in two variables.

Solve A = P + Prt for t.

What is the sum of the measures of the three angles of any triangle?

Simplify: 40a 3 8 x 1 4 b  40a 4 5 b

Evaluate: -4 + 5 - (-3) - 13

Find a linear inequality that has the graph shown. y x 111 1 2 3 4 2 3 4 23 2 3 4 5

Graph the inequality: 4x 3(x  2y 1)  61y 1 22 4

A set of ordered pairs is called a ______ .

A ______ is a rule that assigns to each -value exactly one y-value.

The set of all input values for a function is called the _____ , and the set of all output values is called the _____ .

We can think of a function as a machine that takes some ______ x and turns it into some output _____ .

If (2) = -3, we call -3 a function ______ .

The graph of a _____ function is a straight line and the graph of an _____ value function is V-shaped.

Federal Minimum Hourly Wage. The following table is an example of a function. Use an arrow diagram to illustrate this. Year 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 Minimum 4.25 4.25 4.75 5.15 5.15 5.15 5.15 5.15 6.55 7.25 wage ($)

The arrow diagram describes a function. What is the domain and what is the range of the function? 6 7 8 0 1 2

For the given input, what value will the function machine output? 5 ? f(x) = x2 + 8

a. Fill in the blank: If a line intersects a graph in more than one point, the graph is not the graph of a function. b. Give the coordinates of the points where the given vertical line intersects the graph. c. Is this the graph of a function? x 111 1 2 3 4 5 2 3 4 5 2345

We read (x)  5x 6 ______ as is minus 6.

Since y = ________ , the following two equations are equivalent: y  3x  2 and (x)  3x  2.

The notation (4)  5 x indicates that when the x-value is input into a function rule, the output is . This fact can be shown graphically by plotting the ordered pair ( ).

When graphing the function (x)  x  5, the vertical axis of the coordinate system can be labeled or .

Find the domain and range of each relation. See Example 1. {(6, 1), (1, 10), (6, 2), (8, 5)}

Find the domain and range of each relation. See Example 1. {(11, 3), (0, 0), (4, 5), (3, 7)} {(6

Find the domain and range of each relation. See Example 1. {(0, 9), (8, 50), (6, 9)}

Find the domain and range of each relation. See Example 1. {(1, 12), (6, 8), (5, 8)}

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. 10 20 30 20 40 60 x

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. x y 4 2 0 6 8 10 12

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. x y 1 4 2 4 6

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. x y 5 10 15 15

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. 1 7 2 15 3 23 4 16 5 8 yx

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. 30 2 30 4 30 6 30 8 30 10 yx

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. 0 0 2 4 1 2 3 1 4 yx 1 1

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. 1 1 2 2 3 3 4 4 yx

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. 3 4 3 4 3 4 3 4 yx 1

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. 1 1 1 1 9 1 7 5 3 1 yx 6 0

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. 6 0 1 9 5 4 3 8 yx 1

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. 1.6 0 2.5 20 0.1 1.6 19 7 3 1 yx 3

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. {(3, 4), (3, 4), (4, 3), (4, 3)} 29

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. {(1, 1), (3, 1), (5, 1), (7, 1), (9, 1)} {(3,

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. {(2, 7), (1, 10), (0, 13), (1, 16)}

Determine whether the relation defines to be a function of . If a function is defined, give its domain and range. If it does not define a function, find two ordered pairs that show a value of that is assigned more than one value of . See Example 2. {(2, 4), (3, 8), (3, 12), (4, 16)} {(2,

Find each function value. See Examples 3 and 4. (x)  4x 1 a. (1) b. (2) c. 1 4 d. (50)

Find each function value. See Examples 3 and 4. (x)  1 5x a. (0) b. (75) c. (0.2) d. a4 5

Find each function value. See Examples 3 and 4. (x)  2x2 a. (0.4) b. (3) c. (1,000) d. a 1 8

Find each function value. See Examples 3 and 4. g(x)  6 x2 5 a. g(30) b. g(6) c. g(1) d. g(0.5)

Find each function value. See Examples 3 and 4. h(x)  0 x 7 0 a. h(0) b. h(7) c. h(7) d. h(8)

Find each function value. See Examples 3 and 4. (x)  0 2  x a. (0) b. (2) c. (2) d. (99)

Find each function value. See Examples 3 and 4. g(x)  x3 x a. g(1) b. g(10) c. g(3) d. g(6)

Find each function value. See Examples 3 and 4. g(x)  x4  x a. g(1) b. g(2) c. g(0) d. g(10)

Find each function value. See Examples 3 and 4. s(x)  (x  3)2 a. s(3) b. s(3) s c. s(0) d. s(5)

Find each function value. See Examples 3 and 4. s(x)  (x 8)2 a. s(8) b. s(8) s c. s(1) s d. s(12)

If (x)  3.4x 2 1.2x  0.5, find (0.3).

If g(x)  x 4 x3  x2 x find g(12)

Complete each table of function values and then graph each function. See Examples 5 and 6. (x)  3x 2 4 0 1 1 2 x f(

Complete each table of function values and then graph each function. See Examples 5 and 6. (x)  2x  8 0 1 2 1 x f

Complete each table of function values and then graph each function. See Examples 5 and 6. h(x)  0 1 x 0 0 1 2 3 4 1 2 x h(

Complete each table of function values and then graph each function. See Examples 5 and 6. h(x)  0 x  2 0 0 1 1 2 3 4 5 x h(x)

Graph each function. See Examples 5 and 6. (x)  x  3 1 2 x 2

Graph each function. See Examples 5 and 6. (x)  2 3 (x)  x  3

Graph each function. See Examples 5 and 6. h(x)  0 x 0 g

Graph each function. See Examples 5 and 6. g(x)  0 x 0 2

Determine whether each graph is the graph of a function. If it is not, find ordered pairs that show a value of that is assigned more than one value of . See Example 7. y 111 1 2 3 4 2 3 4 234 2 3 4

Determine whether each graph is the graph of a function. If it is not, find ordered pairs that show a value of that is assigned more than one value of . See Example 7. y 111 1 2 3 4 2 3 4 234 2 3 4

Determine whether each graph is the graph of a function. If it is not, find ordered pairs that show a value of that is assigned more than one value of . See Example 7. y 111 1 2 3 4 5 2 3 234 2 3 4

Determine whether each graph is the graph of a function. If it is not, find ordered pairs that show a value of that is assigned more than one value of . See Example 7. y 111 1 2 3 4 2 3 4 234 2 3 4

Determine whether each graph is the graph of a function. If it is not, find ordered pairs that show a value of that is assigned more than one value of . See Example 7. y 111 1 2 3 4 2 3 4 234 2 3 4

Determine whether each graph is the graph of a function. If it is not, find ordered pairs that show a value of that is assigned more than one value of . See Example 7. y 111 1 2 3 4 2 3 4 234 2 3 4

Determine whether each graph is the graph of a function. If it is not, find ordered pairs that show a value of that is assigned more than one value of . See Example 7. x 111 1 2 3 4 2 3 4 23 2 54

Determine whether each graph is the graph of a function. If it is not, find ordered pairs that show a value of that is assigned more than one value of . See Example 7. y x 111 1 2 3 4 2 3 4 234 2 3 4

Reflections. When a beam of light hits a mirror, it is reflected off the mirror at the same angle that the incoming beam struck the mirror. What type of function could serve as a mathematical model for the path of the light beam shown here? 45 45 Mirror Li

Lightning. The function D(t)  t 5 gives the approximate distance in miles that you are from a lightning strike, where is the number of seconds between seeing the lightning and hearing the thunder. Find and explain what it means.

Vacationing. The function C(d)  500  100(d 3) gives the cost in dollars to rent an RV motor home for days. (The terms of the rental agreement require a 3-day minimum.) Find the cost of renting the RV for a vacation that will last 7 days.

Structural Engineering. The maximum safe load in pounds of the rectangular beam shown in the figure is given by the function S(t)  t 1,875t 2 8, where is the thickness of the beam, in inches. Find the maximum safe load if the beam is 4 inches thick. t inches Load

Lawn Sprinklers. The function A(r)  pr 2 can be used to determine the area in square feet that will be watered by a rotating sprinkler that sprays out a stream of water. Find and . Round to the nearest tenth.

Parts Lists. The function (r)  2.30  3.25(r  0.40) approximates the length (in feet) of the belt that joins the two pulleys, where is the radius (in feet) of the smaller pulley. Find the belt length needed for each pulley in the parts list. r ft 0.40 ft Parts list Pulley Belt length P-45M 0.32 P-08D 0.24

Postage. The step graph below shows how the cost of a first class U.S. postage stamp increased from 1990 through 2010. An open circle at the end of a line segment means the endpoint of the segment is not included. Is this the graph of a function? Postal Rate U.S. First Class Stamp 0 25 30 35 40 45 1990 1995 2000 2005 2010 Year Po

Sound. We cannot see sound waves, but certain scientific instruments are used to draw mathematical models of them. Is the graph of a sound wave shown below a function? y x 10 20 30 40 50 0 1 5 0 15 Time (sec) 20 25 10 20 30 40 50

In the function y  5x  2 x, why do you think the value of is called the input and the corresponding value of the output?

Explain what a politician meant when she said, The speed at which the downtown area will be redeveloped is a function of the number of low-interest loans made available to the property owners.

Explain the following diagram: f(4)  11 (4, 11)

Explain the error in the following solution. If , find  101  7x  100  7x  1 f(10)  102  7x  1 f(x)  x f(10).

A student was asked to determine whether the graph on the right is the graph of a function. What is wrong with the following reasoning? When I draw a vertical line through the graph, it intersects the graph only once. By the vertical line test, this is the graph of a function. y x 111 1 2 3 4 2 3 4 234 2 3 4

In your own words, what is a function?

Coffee Blends. A store sells regular coffee for $4 a pound and gourmet coffee for $7 a pound. To get rid of 40 pounds of the gourmet coffee, the shopkeeper plans to make a gourmet blend that he will put on sale for $5 a pound. How many pounds of regular coffee should be used?

Photographic Chemicals. A photographer wishes to mix 2 liters of a 5% acetic acid solution with a 10% acetic solution to get a 7% acetic solution. How many liters of 10% acetic solution must be added?

Is the graph of y  3 x a function? Explain. y x y 3 x 111 1 2 3 4 2 3 4 2 2 3 4 5 6

If (x)  x r2 2  x, find 1 4 5 r

Let (x)  2x  5 x. For what value of x is (x)  7?

Let and (x)  x 2 and g(x)  3x. Find . (g(6))

Graph the points with coordinates (1, 3), (0, 1.5), (4, 4), 2, 7 2, and (4, 0) .

Hawaii. Estimate the coordinates of Oahu using an ordered pair of the form (longitude, latitude). 160 Kauai Oahu Lanai Maui Hawaii 19 20 21 22

In what quadrant does the point (-3, -4) lie?

What are the coordinates of the origin?

Geometry. Three vertices (corners) of a square are (-5, 4), (-5, -2) and (1, -2). Find the coordinates of the fourth vertex and then find the area of the square.

College Enrollments. The graph gives the number of students enrolled at a college for the period from 4 weeks before to 5 weeks after the semester began. a. What was the maximum enrollment and when did it occur? b. How many students were enrolled 2 weeks before the semester began? c. When was the enrollment 2,250? 0 1,000 1,500 2,000 2,500 4 23 2345 Semester begins Week of the semester Nu

Is (3, 2) a solution of y 2x 4?

Complete the table of solutions. 3x 2y 18 3 2 yx (x, y) y

Which of the following equations are not linear equations? 8x  2y 6 y x2 1 y x y  x3 0

The graph of a linear equation is shown. a. When the coordinates of point are substituted into the equation, will a true or false statement result? b. When the coordinates of point are substituted into the equation, will a true or false statement result? x A B 111 1 2 3 4 2 3 4 234

Graph each equation by constructing a table of solutions. y 4x  2 x

Graph each equation by constructing a table of solutions. y 3 4 x

Graph each equation by constructing a table of solutions. 5y 5x 15 y (Hint: Solve for first.)

Graph each equation by constructing a table of solutions. 6y 4x y (Hint: Solve for first.)

Birthday Parties. A restaurant offers a party package for children that includes everything: food, drinks, cake, and favors. The cost , in dollars, is given by the equation c 8n 50 6, where is the number of children attending the party. Graph the equation and use the graph to estimate the cost of a party if 18 children attend.

Determine whether each statement is true or false. a. It takes three or more points to determine a line. b. A linear equation in two variables has infinitely many solutions.

Identify the - and -intercepts of the graph shown in figure (a) below. y x 111 1 2 3 4 2 3 4 234 ,000 20,000 30,000 4 6 8 10 Age of equipment (years) Value of sound equipment

Depreciation. The graph in figure (b) above shows how the value of some sound equipment decreased over the years. Find the intercepts of the graph. What information do the intercepts give about the equipment?

Use the intercept method to graph each equation. 4x 2y 8 Th

Use the intercept method to graph each equation. 5x  4y 13

Use the intercept method to graph each equation. Graph: y = 4

Use the intercept method to graph each equation. Graph: x = -1

In each case, find the slope of the line. y 111 1 2 3 4 2 3 4 234 2 3 4

In each case, find the slope of the line. y 111 1 2 3 4 2 3 4 234 2 3 4

The line with this table of solutions: 2 4 17 (4, 17) 3 (2, 3) yx

The line passing through the points (1, -4) and (3, -7).

Draw a line having a slope that is a. Positive b. Negative c. 0 d. Undefined

Carpentry. If a truss like the one shown below is used to build the roof of a shed, find the slope (pitch) of the roof. 6 ft 16 ft

Ramps. Find the grade of the ramp shown below. Round to the nearest tenth of a percent. 24 ft 2 ft

Bottled Water. Refer to the graph below. Find the rate of change in the amount of bottled water consumed per person in the U.S. from 2000 through 2008. 00 01 02 03 04 05 06 07 08 Year U.S. Bottled Water Consumption Gallons per person

Without graphing, determine whether the line that passes through (6, 6) and (4, 2) and the line that passes through (2, -10) and (-2, -2) are parallel, perpendicular, or neither.

Find the slope of a line perpendicular to the line passing through (-1, 9) and (-8, 4).

Find the slope and the y-intercept of each line. y 3 4 x  2

Find the slope and the y-intercept of each line. y = -4x

Find the slope and the y-intercept of each line. y x 8 10 y

Find the slope and the y-intercept of each line. 7x 5y 21 y

Graph the line with slope -4 and y-intercept (0, -1). Write an equation of the line.

Write an equation for the line shown here. y x 11234 1 1 2 3 4 2 3 234

Find the slope and the -intercept of the line whose equation is 9x  3y 15. Then graph it.

Copiers. A business buys a used copy machine that has already produced 75,000 copies. a. If the business plans to run 300 copies a week, write a linear equation that would find the number of copies the machine has made in its lifetime after the business has used it for weeks. b. Use your result in part a to predict the total number of copies that will have been made on the machine 1 year, or 52 weeks, after being purchased by the business.

Without graphing, determine whether graphs of the given pairs of lines are parallel, perpendicular, or neither. y  2 3 x 6 y 2 3 x  6

Without graphing, determine whether graphs of the given pairs of lines are parallel, perpendicular, or neither. x 5y 10 y  5x 0

Find an equation of the line with the given slope that passes through the given point. Write the equation in slopeintercept form and graph the equation. m 3, (1, 5)

Find an equation of the line with the given slope that passes through the given point. Write the equation in slopeintercept form and graph the equation. m 1 2 , (4, 1)

Find an equation of the line with the following characteristics. Write the equation in slopeintercept form. Passing through (3, 7) and (-6, 1)

Find an equation of the line with the following characteristics. Write the equation in slopeintercept form. Horizontal, passing through (6, -8)

Car Registration. When it was 2 years old, the annual registration fee for a Dodge Caravan was $380. When it was 4 years old, the registration fee dropped to $310. If the relationship is linear, write an equation that gives the registration fee f in dollars for the van when it is years old.

The Atmosphere. The scatter diagram below shows the amount of carbon dioxide in the Earth's atmosphere as measured at Hawaii's Mauna Loa Observatory from 1960 through 2010. A straight line can be used to model the data. a. Use the two highlighted points in red to write the equation of the line. Write the answer in slopeintercept form. b. Use your answer to part a to predict the amount of carbon dioxide in the atmosphere in 2020. P t 0 (1960) 320 340 360 370 380 390 310 330 350 10 20 30 40 50 (2010) 60 Years after 1960 Source: National Oceanic and Atmospheric Administration Carbon dioxide (parts per million)

Determine whether each ordered pair is a solution of 2x  y 4 a. (0, 5) b. (2, 8) c. (3, 2) d. 1 2 5

Fill in the blanks: 2x  3y  6 means 2x  3y 6 or 2x  3y 6.

Graph each inequality. x  y  5 2

Graph each inequality. 2x  3y  6

Graph each inequality. y 2x

Graph each inequality. y  4

The graph of a linear inequality is shown in the next column. Would a true or a false statement result if the coordinates of a. point were substituted into the inequality? b. point were substituted into the inequality? c. point were substituted into the inequality? y x B C A 111 1 2 3 2 3 4 5 23 2 3 4

Work Schedules. A student told her employer that during the school year, she would be available for up to 30 hours a week, working either 3- or 5-hour shifts. If represents the number of 3-hour shifts she works and represents the number of 5-hour shifts she works, the inequality 3x 5y 30 shows the possible combinations of shifts she can work. Graph the inequality and find three possible combinations.

Find the domain and range of each relation. {(7, 3), (5, 9), (4, 4), (0, 11)}

Find the domain and range of each relation. {(2, 2), (15, 8), (6, 9), (1, 8)}

Determine whether each relation defines y to be function of x. If a function is defined, give its domain and range. If it does not define a function, find ordered pairs that show a value of x that corresponds to more than one value of y. 4 8 6 9 0 x

Determine whether each relation defines y to be function of x. If a function is defined, give its domain and range. If it does not define a function, find ordered pairs that show a value of x that corresponds to more than one value of y. 6 5 3 2 4 1 x

Determine whether each relation defines y to be function of x. If a function is defined, give its domain and range. If it does not define a function, find ordered pairs that show a value of x that corresponds to more than one value of y. 9 81 7 49 5 25 3 9 yx

Determine whether each relation defines y to be function of x. If a function is defined, give its domain and range. If it does not define a function, find ordered pairs that show a value of x that corresponds to more than one value of y. 2 0 3 4 1 5 1 1 yx

Determine whether each relation defines y to be function of x. If a function is defined, give its domain and range. If it does not define a function, find ordered pairs that show a value of x that corresponds to more than one value of y. {(1, 6), (0, 6), (1, 6), (2, 6)}

Determine whether each relation defines y to be function of x. If a function is defined, give its domain and range. If it does not define a function, find ordered pairs that show a value of x that corresponds to more than one value of y. {(4, 4), (6, 4), (4, 6)}

The set of all input values for a function is called the _____, and the set of all output values is called the _____ .

Fill in the blank: Since y y the equations a y 2x  8D and (x) 2x  8y are equivalent.

For f(x) = x2 - 4x, find each of the following function values. (1)

For f(x) = x2 - 4x, find each of the following function values. (0)

For f(x) = x2 - 4x, find each of the following function values. (3) b

For f(x) = x2 - 4x, find each of the following function values. a 1 2

For g(x) = 1 - 6x, find each of the following function values. g(1)

For g(x) = 1 - 6x, find each of the following function values. g(6)

For g(x) = 1 - 6x, find each of the following function values. g(0.5)

For g(x) = 1 - 6x, find each of the following function values. ga 3 2

Determine whether each graph is the graph of a function. If it is not, find two ordered pairs that show a value of x that corresponds to more than one value of y. y 111 1 2 3 4 2 3 4 234 2 3 4

Determine whether each graph is the graph of a function. If it is not, find two ordered pairs that show a value of x that corresponds to more than one value of y. y x 111 1 2 3 4 2 3 4 234 2 3 4

Complete the table of function values for f (x) 1  x y. Then graph the function. 0 1 3 3 1 x

Aluminum Cans. The function V(r) 15.7r2 estimates the volume in cubic inches of a can 5 inches tall with a radius of inches. Find the volume of the can shown in the illustration. 5 in. 8 in.