In Exercises 8796, write the slope-intercept forms of the equations of the lines through

Fill in the blanks. The simplest mathematical model for relating two variables is the ________ equation in two variables

Fill in the blanks. For a line, the ratio of the change in to the change in is called the ________ of the line.

Fill in the blanks. Two lines are ________ if and only if their slopes are equal.

Fill in the blanks. Two lines are ________ if and only if their slopes are negative reciprocals of each other.

Fill in the blanks. When the -axis and -axis have different units of measure, the slope can be interpreted as a ________.

Fill in the blanks. The prediction method ________ ________ is the method used to estimate a point on a line when the point does not lie between the given points.

Fill in the blanks. Every line has an equation that can be written in ________ form.

Fill in the blanks. Match each equation of a line with its form. (a) (i) Vertical line (b) (ii) Slope-intercept form (c) (iii) General form (d) (iv) Point-slope form (e) (v) Horizontal line

In Exercises 9 and 10, identify the line that has each slope.

In Exercises 9 and 10, identify the line that has each slope.

In Exercises 11 and 12, sketch the lines through the point with the indicated slopes on the same set of coordinate axes.

In Exercises 11 and 12, sketch the lines through the point with the indicated slopes on the same set of coordinate axes.

In Exercises 1316, estimate the slope of the line.

In Exercises 1316, estimate the slope of the line.

In Exercises 1316, estimate the slope of the line.

In Exercises 1316, estimate the slope of the line.

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 1728, find the slope and -intercept (if possible) of the equation of the line. Sketch the line

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 2940, plot the points and find the slope of the line passing through the pair of points.

In Exercises 4150, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)

In Exercises 4150, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)

In Exercises 4150, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)

In Exercises 4150, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)

In Exercises 4150, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)

In Exercises 4150, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)

In Exercises 4150, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)

In Exercises 4150, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)

In Exercises 4150, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)

In Exercises 4150, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 51 64, find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 6578, find the slope-intercept form of the equation of the line passing through the points. Sketch the line.

In Exercises 79 82, determine whether the lines are parallel, perpendicular, or neither.

In Exercises 79 82, determine whether the lines are parallel, perpendicular, or neither.

In Exercises 79 82, determine whether the lines are parallel, perpendicular, or neither.

In Exercises 79 82, determine whether the lines are parallel, perpendicular, or neither.

In Exercises 8386, determine whether the lines and passing through the pairs of points are parallel, perpendicular, or neither.

In Exercises 8386, determine whether the lines and passing through the pairs of points are parallel, perpendicular, or neither.

In Exercises 8386, determine whether the lines and passing through the pairs of points are parallel, perpendicular, or neither.

In Exercises 8386, determine whether the lines and passing through the pairs of points are parallel, perpendicular, or neither.

In Exercises 8796, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

In Exercises 8796, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

In Exercises 8796, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

In Exercises 8796, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

In Exercises 8796, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

In Exercises 8796, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

In Exercises 8796, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

In Exercises 8796, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

In Exercises 8796, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

In Exercises 8796, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.

In Exercises 97102, use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts and is -intercept:

In Exercises 97102, use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts and is -intercept: -intercept: -intercept:

In Exercises 97102, use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts and is -intercept:

In Exercises 97102, use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts and is -intercept: -intercept: -intercept:

In Exercises 97102, use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts and is Point on line: -intercept: -intercept:

In Exercises 97102, use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts and is Point on line: -intercept: -intercept:

GRAPHICAL ANALYSIS In Exercises 103106, identify any relationships that exist among the lines, and then use a graphing utility to graph the three equations in the same viewing window. Adjust the viewing window so that the slope appears visually correctthat is, so that parallel lines appear parallel and perpendicular lines appear to intersect at right angles.

GRAPHICAL ANALYSIS In Exercises 103106, identify any relationships that exist among the lines, and then use a graphing utility to graph the three equations in the same viewing window. Adjust the viewing window so that the slope appears visually correctthat is, so that parallel lines appear parallel and perpendicular lines appear to intersect at right angles.

GRAPHICAL ANALYSIS In Exercises 103106, identify any relationships that exist among the lines, and then use a graphing utility to graph the three equations in the same viewing window. Adjust the viewing window so that the slope appears visually correctthat is, so that parallel lines appear parallel and perpendicular lines appear to intersect at right angles.

GRAPHICAL ANALYSIS In Exercises 103106, identify any relationships that exist among the lines, and then use a graphing utility to graph the three equations in the same viewing window. Adjust the viewing window so that the slope appears visually correctthat is, so that parallel lines appear parallel and perpendicular lines appear to intersect at right angles.

In Exercises 107110, find a relationship between and such that is equidistant (the same distance) from the two points

In Exercises 107110, find a relationship between and such that is equidistant (the same distance) from the two points

In Exercises 107110, find a relationship between and such that is equidistant (the same distance) from the two points

In Exercises 107110, find a relationship between and such that is equidistant (the same distance) from the two points

SALES The following are the slopes of lines representing annual sales in terms of time in years. Use the slopes to interpret any change in annual sales for a one-year increase in time. (a) The line has a slope of (b) The line has a slope of (c) The line has a slope of

REVENUE The following are the slopes of lines representing daily revenues in terms of time in days. Use the slopes to interpret any change in daily revenues for a one-day increase in time. (a) The line has a slope of (b) The line has a slope of (c) The line has a slope of

AVERAGE SALARY The graph shows the average salaries for senior high school principals from 1996 through 2008. (Source: Educational Research Service) (a) Use the slopes of the line segments to determine the time periods in which the average salary increased the greatest and the least. (b) Find the slope of the line segment connecting the points for the years 1996 and 2008. (c) Interpret the meaning of the slope in part (b) in the context of the problem.

SALES The graph shows the sales (in billions of dollars) for Apple Inc. for the years 2001 through 2007. (Source: Apple Inc.) (a) Use the slopes of the line segments to determine the years in which the sales showed the greatest increase and the least increase. (b) Find the slope of the line segment connecting the points for the years 2001 and 2007. (c) Interpret the meaning of the slope in part (b) in the context of the problem.

ROAD GRADE You are driving on a road that has a 6% uphill grade (see figure). This means that the slope of the road is Approximate the amount of vertical change in your position if you drive 200 feet.

ROAD GRADE From the top of a mountain road, a surveyor takes several horizontal measurements and several vertical measurements as shown in the table ( and are measured in feet). (a) Sketch a scatter plot of the data. (b) Use a straightedge to sketch the line that you think best fits the data. (c) Find an equation for the line you sketched in part (b). (d) Interpret the meaning of the slope of the line in part (c) in the context of the problem. (e) The surveyor needs to put up a road sign that indicates the steepness of the road. For instance, a surveyor would put up a sign that states 8% grade on a road with a downhill grade that has a slope of What should the sign state for the road in this problem?

$2540 $125 decrease per year

$156 $4.50 increase per year

DEPRECIATION The value of a molding machine years after it is purchased is Explain what the -intercept and the slope measure.

COST The cost of producing computer laptop bags is given by Explain what the -intercept and the slope measure.

DEPRECIATION A sub shop purchases a used pizza oven for $875. After 5 years, the oven will have to be replaced. Write a linear equation giving the value of the equipment during the 5 years it will be in use.

DEPRECIATION A school district purchases a high-volume printer, copier, and scanner for $25,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2000. Write a linear equation giving the value of the equipment during the 10 years it will be in use.

SALES A discount outlet is offering a 20% discount on all items. Write a linear equation giving the sale price for an item with a list price

HOURLY WAGE A microchip manufacturer pays its assembly line workers $12.25 per hour. In addition, workers receive a piecework rate of $0.75 per unit produced. Write a linear equation for the hourly wage in terms of the number of units produced per hour.

MONTHLY SALARY A pharmaceutical salesperson receives a monthly salary of $2500 plus a commission of 7% of sales. Write a linear equation for the salespersons monthly wage in terms of monthly sales

BUSINESS COSTS A sales representative of a company using a personal car receives $120 per day for lodging and meals plus $0.55 per mile driven. Write a linear equation giving the daily cost to the company in terms of the number of miles driven.

CASH FLOW PER SHARE The cash flow per share for the Timberland Co. was $1.21 in 1999 and $1.46 in 2007. Write a linear equation that gives the cash flow per share in terms of the year. Let represent 1999. Then predict the cash flows for the years 2012 and 2014. (Source: The Timberland Co.)

NUMBER OF STORES In 2003 there were 1078 J.C. Penney stores and in 2007 there were 1067 stores. Write a linear equation that gives the number of stores in terms of the year. Let represent 2003. Then predict the numbers of stores for the years 2012 and 2014. Are your answers reasonable? Explain. (Source: J.C. Penney Co.)

COLLEGE ENROLLMENT The Pennsylvania State University had enrollments of 40,571 students in 2000 and 44,112 students in 2008 at its main campus in University Park, Pennsylvania. (Source: Penn State Fact Book) (a) Assuming the enrollment growth is linear, find a linear model that gives the enrollment in terms of the year where corresponds to 2000. (b) Use your model from part (a) to predict the enrollments in 2010 and 2015. (c) What is the slope of your model? Explain its meaning in the context of the situation.

COLLEGE ENROLLMENT The University of Florida had enrollments of 46,107 students in 2000 and 51,413 students in 2008. (Source: University of Florida) (a) What was the average annual change in enrollment from 2000 to 2008? (b) Use the average annual change in enrollment to estimate the enrollments in 2002, 2004, and 2006. (c) Write the equation of a line that represents the given data in terms of the year where corresponds to 2000. What is its slope? Interpret the slope in the context of the problem. (d) Using the results of parts (a)(c), write a short paragraph discussing the concepts of slope and average rate of change.

COST, REVENUE, AND PROFIT A roofing contractor purchases a shingle delivery truck with a shingle elevator for $42,000. The vehicle requires an average expenditure of $6.50 per hour for fuel and maintenance, and the operator is paid $11.50 per hour. (a) Write a linear equation giving the total cost of operating this equipment for hours. (Include the purchase cost of the equipment.) (b) Assuming that customers are charged $30 per hour of machine use, write an equation for the revenue derived from hours of use. (c) Use the formula for profit to write an equation for the profit derived from hours of use. (d) Use the result of part (c) to find the break-even pointthat is, the number of hours this equipment must be used to yield a profit of 0 dollars.

RENTAL DEMAND A real estate office handles an apartment complex with 50 units. When the rent per unit is $580 per month, all 50 units are occupied. However, when the rent is $625 per month, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent and the demand is linear. (a) Write the equation of the line giving the demand in terms of the rent (b) Use this equation to predict the number of units occupied when the rent is $655. (c) Predict the number of units occupied when the rent is $595.

GEOMETRY The length and width of a rectangular garden are 15 meters and 10 meters, respectively. A walkway of width surrounds the garden. (a) Draw a diagram that gives a visual representation of the problem. (b) Write the equation for the perimeter of the walkway in terms of (c) Use a graphing utility to graph the equation for the perimeter. (d) Determine the slope of the graph in part (c). For each additional one-meter increase in the width of the walkway, determine the increase in its perimeter.

AVERAGE ANNUAL SALARY The average salaries (in millions of dollars) of Major League Baseball players from 2000 through 2007 are shown in the scatter plot. Find the equation of the line that you think best fits these data. (Let represent the average salary and let represent the year, with corresponding to 2000.) (Source: Major League Baseball Players Association)

DATA ANALYSIS: NUMBER OF DOCTORS The numbers of doctors of osteopathic medicine (in thousands) in the United States from 2000 through 2008, where is the year, are shown as data points (Source: American Osteopathic Association) , , , , , , , , (a) Sketch a scatter plot of the data. Let correspond to 2000. (b) Use a straightedge to sketch the line that you think best fits the data. (c) Find the equation of the line from part (b). Explain the procedure you used. (d) Write a short paragraph explaining the meanings of the slope and -intercept of the line in terms of the data. (e) Compare the values obtained using your model with the actual values. (f ) Use your model to estimate the number of doctors of osteopathic medicine in 2012.

DATA ANALYSIS: AVERAGE SCORES An instructor gives regular 20-point quizzes and 100-point exams in an algebra course. Average scores for six students, given as data points where is the average quiz score and is the average test score, are and [Note: There are many correct answers for parts (b)(d).] (a) Sketch a scatter plot of the data. (b) Use a straightedge to sketch the line that you think best fits the data. (c) Find an equation for the line you sketched in part (b). (d) Use the equation in part (c) to estimate the average test score for a person with an average quiz score of 17. (e) The instructor adds 4 points to the average test score of each student in the class. Describe the changes in the positions of the plotted points and the change in the equation of the line.

A line with a slope of is steeper than a line with a slope of

The line through and and the line through and are parallel.

Explain how you could show that the points and are the vertices of a right triangle.

Explain why the slope of a vertical line is said to be undefined.

With the information shown in the graphs, is it possible to determine the slope of each line? Is it possible that the lines could have the same slope? Explain. (a) (b)

The slopes of two lines are and Which is steeper? Explain.

Use a graphing utility to compare the slopes of the lines where 1, 2, and 4. Which line rises most quickly? Now, let and Which line falls most quickly? Use a square setting to obtain a true geometric perspective. What can you conclude about the slope and the rate at which the line rises or falls?

Find and in terms of and respectively (see figure). Then use the Pythagorean Theorem to find a relationship between and

THINK ABOUT IT Is it possible for two lines with positive slopes to be perpendicular? Explain.

CAPSTONE Match the description of the situation with its graph. Also determine the slope and -intercept of each graph and interpret the slope and -intercept in the context of the situation. [The graphs are labeled (i), (ii), (iii), and (iv).] (i) (ii) (iii) (iv) (a) A person is paying $20 per week to a friend to repay a $200 loan. (b) An employee is paid $8.50 per hour plus $2 for each unit produced per hour. (c) A sales representative receives $30 per day for food plus $0.32 for each mile traveled. (d) A computer that was purchased for $750 depreciates $100 per year.