Use the discriminant to determine the number and

Give the coordinates for each point labeled. Point A

Give the coordinates for each point labeled. Point B

Give the coordinates for each point labeled. Point C

Give the coordinates for each point labeled. Point D

Give the coordinates for each point labeled. Point E

Give the coordinates for each point labeled. Point F

Plot each point in the Cartesian plane and indicate in which quadrant or on which axis the point lies. A: (2, 3) B: (1, 4) C: (3, 3) D: (5, 1) E: (0, 2) F: (4, 0)

Plot each point in the Cartesian plane and indicate in which quadrant or on which axis the point lies. A: (2, 3) B: (1, 4) C: (3, 3) D: (5, 1) E: (0, 2) F: (4, 0)

Plot the points (3, 1), (3, 4), (3, 2), (3, 0), (3, 4). Describe the line containing points of the form (3, y).

Plot the points (1, 2), (3, 2), (0, 2), (3, 2), (5, 2). Describe the line containing points of the form (x, 2).

Calculate the distance between the given points, and nd the midpoint of the segment joining them. (1, 3) and (5, 3)

Calculate the distance between the given points, and nd the midpoint of the segment joining them. (2, 4) and (2, 4)

Calculate the distance between the given points, and nd the midpoint of the segment joining them. (1, 4) and (3, 0)

Calculate the distance between the given points, and nd the midpoint of the segment joining them. (3, 1) and (1, 3)

Calculate the distance between the given points, and nd the midpoint of the segment joining them. (10, 8) and (7, 1)

Calculate the distance between the given points, and nd the midpoint of the segment joining them. (2, 12) and (7, 15)

Calculate the distance between the given points, and nd the midpoint of the segment joining them. (3, 1) and (7, 2)

Calculate the distance between the given points, and nd the midpoint of the segment joining them. (4, 5) and (9, 7)

Calculate the distance between the given points, and nd the midpoint of the segment joining them. (6, 4) and (2, 8)

Calculate the distance between the given points, and nd the midpoint of the segment joining them. (0, 7) and (4, 5)

Calculate the distance between the given points, and nd the midpoint of the segment joining them.

Calculate the distance between the given points, and nd the midpoint of the segment joining them.

Calculate the distance between the given points, and nd the midpoint of the segment joining them.

Calculate the distance between the given points, and nd the midpoint of the segment joining them.

Calculate the distance between the given points, and nd the midpoint of the segment joining them.

Calculate the distance between the given points, and nd the midpoint of the segment joining them.

Calculate the distance between the given points, and nd the midpoint of the segment joining them.

Calculate the distance between the given points, and nd the midpoint of the segment joining them.

Calculate the distance between the given points, and nd the midpoint of the segment joining them.

Calculate the distance between the given points, and nd the midpoint of the segment joining them.

Calculate the distance between the given points, and nd the midpoint of the segment joining them.

Calculate the distance between the given points, and nd the midpoint of the segment joining them. (215, 4) and (1, 213)

Calculate (to two decimal places) the perimeter of the triangle with the following vertices: Points A, B, and C

Calculate (to two decimal places) the perimeter of the triangle with the following vertices: Points C, D, and E

determine whether the triangle with the given vertices is a right triangle, an isosceles triangle, neither, or both. (Recall that a right triangle satises the Pythagorean theorem and an isosceles triangle has at least two sides of equal length.) (0, 3), (3, 3), and (3, 5)

determine whether the triangle with the given vertices is a right triangle, an isosceles triangle, neither, or both. (Recall that a right triangle satises the Pythagorean theorem and an isosceles triangle has at least two sides of equal length.) (0, 2), (2, 2), and (2, 2)

determine whether the triangle with the given vertices is a right triangle, an isosceles triangle, neither, or both. (Recall that a right triangle satises the Pythagorean theorem and an isosceles triangle has at least two sides of equal length.) (1, 1), (3, 1), and (2, 4)

determine whether the triangle with the given vertices is a right triangle, an isosceles triangle, neither, or both. (Recall that a right triangle satises the Pythagorean theorem and an isosceles triangle has at least two sides of equal length.) (3, 3), (3, 3), and (3, 3)

Cell Phones. A cellular phone company currently has three towers: one in Tampa, one in Orlando, and one in Gainesville to serve the central Florida region. If Orlando is 80 miles east of Tampa and Gainesville is 100 miles north of Tampa, what is the distance from Orlando to Gainesville?

Cell Phones. The same cellular phone company in Exercise 39 has decided to add additional towers at each halfway between cities. How many miles from Tampa is each halfway tower?

Travel. A retired couple who live in Columbia, South Carolina, decide to take their motor home and visit two children who live in Atlanta and in Savannah, Georgia. Savannah is 160 miles south of Columbia, and Atlanta is 215 miles west of Columbia. How far apart do the children live from each other?

Sports. In the 1984 Orange Bowl, Doug Flutie, the 5 foot 9 inch quarterback for Boston College, shocked the world as he threw a hail Mary pass that was caught in the end zone with no time left on the clock, defeating the Miami Hurricanes 4745. Although the record books have it listed as a 48 yard pass, what was the actual distance the ball was thrown? The following illustration depicts the path of the ball.

NASCAR Revenue. Action Performance Inc., the leading seller of NASCAR merchandise, recorded $260 million in revenue in 2002 and $400 million in revenue in 2004. Calculate the midpoint to estimate the revenue Action Performance Inc. recorded in 2003. Assume the horizontal axis represents the year and the vertical axis represents the revenue in millions.

Ticket Price. In 1993, the average Miami Dolphins ticket price was $28, and in 2001 the average price was $56. Find the midpoint of the segment joining these two points to estimate the ticket price in 1997.

It is often useful to display data in visual form by plotting the data as a set of points. This provides a graphical display between the two variables. The following table contains data on the average monthly price of gasoline. Economics. Create a graph displaying the price of gasoline for the year 2008.

It is often useful to display data in visual form by plotting the data as a set of points. This provides a graphical display between the two variables. The following table contains data on the average monthly price of gasoline. Economics. Create a graph displaying the price of gasoline for the year 2009.

Explain the mistake that is made. Calculate the distance between (2, 7) and (9, 10). Solution: Write the distance formula. Substitute (2, 7) and (9, 10). Simplify. This is incorrect. What mistake was made?

Explain the mistake that is made. Calculate the distance between (2, 1) and (3, 7). Solution: Write the distance formula. Substitute (2, 1) and (3, 7). Simplify. This is incorrect. What mistake was made?

Explain the mistake that is made. Compute the midpoint of the segment with endpoints (3, 4) and (7, 9). Solution: Write the midpoint formula. (xm, ym) = a x1 + x2 2 , y1 + y2 2 b CATCH THE MISTAKE Substitute (3, 4) and (7, 9). Simplify. This is incorrect. What mistake was made?

Explain the mistake that is made. Compute the midpoint of the segment with endpoints (1, 2) and (3, 4). Solution: Write the midpoint formula. Substitute (1, 2) and (3, 4). Simplify. (xm, ym)  (1, 1) This is incorrect. What mistake was made?

determine whether each statement is true or false.he distance from the origin to the point (a, b) is

determine whether each statement is true or false.The midpoint of the line segment joining the origin and the point (a, a) is

determine whether each statement is true or false.The midpoint of any segment joining two points in quadrant I also lies in quadrant I.

determine whether each statement is true or false.The midpoint of any segment joining a point in quadrant I to a point in quadrant III also lies in either quadrant I or III.

determine whether each statement is true or false.Calculate the length and the midpoint of the line segment joining the points (a, b) and (b, a).

determine whether each statement is true or false.Calculate the length and the midpoint of the line segment joining the points (a, b) and (a, b).

Assume that two points (x1, y1) and (x2, y2) are connected by a segment. Prove that the distance from the midpoint of the segment to either of the two points is the same.

Prove that the diagonals of a parallelogram in the gure intersect at their midpoints.

Assume that two points (a, b) and (c, d) are the endpoints of a line segment. Calculate the distance between the two points. Prove that it does not matter which point is labeled as the rst point in the distance formula.

Show that the points (1, 1), (0, 0), and (2, 2) are collinear (lie on the same line) by showing that the sum of the distance from (1, 1) to (0, 0) and the distance from (0, 0) to (2, 2) is equal to the distance from (1, 1) to (2, 2).

calculate the distance between the two points. Use a graphing utility to graph the segment joining the two points and nd the midpoint of the segment. (2.3, 4.1) and (3.7, 6.2)

calculate the distance between the two points. Use a graphing utility to graph the segment joining the two points and nd the midpoint of the segment. (4.9, 3.2) and (5.2, 3.4)

calculate the distance between the two points. Use a graphing utility to graph the segment joining the two points and nd the midpoint of the segment. (1.1, 2.2) and (3.3, 4.4)

calculate the distance between the two points. Use a graphing utility to graph the segment joining the two points and nd the midpoint of the segment. (1.3, 7.2) and (2.3, 4.5)

determine whether each point lies on the graph of the equation.

determine whether each point lies on the graph of the equation.

determine whether each point lies on the graph of the equation.

determine whether each point lies on the graph of the equation.

determine whether each point lies on the graph of the equation.

determine whether each point lies on the graph of the equation.

determine whether each point lies on the graph of the equation.

determine whether each point lies on the graph of the equation.

complete the table and use the table to sketch a graph of the equation.

complete the table and use the table to sketch a graph of the equation.

complete the table and use the table to sketch a graph of the equation.

complete the table and use the table to sketch a graph of the equation.

complete the table and use the table to sketch a graph of the equation.

complete the table and use the table to sketch a graph of the equation.

graph the equation by plotting points.

graph the equation by plotting points.

graph the equation by plotting points.

graph the equation by plotting points.

graph the equation by plotting points.

graph the equation by plotting points.

graph the equation by plotting points.

graph the equation by plotting points.

nd the x-intercept(s) and y-intercepts(s) (if any) of the graphs of the given equations.

nd the x-intercept(s) and y-intercepts(s) (if any) of the graphs of the given equations.

nd the x-intercept(s) and y-intercepts(s) (if any) of the graphs of the given equations.

nd the x-intercept(s) and y-intercepts(s) (if any) of the graphs of the given equations.

nd the x-intercept(s) and y-intercepts(s) (if any) of the graphs of the given equations.

nd the x-intercept(s) and y-intercepts(s) (if any) of the graphs of the given equations.

nd the x-intercept(s) and y-intercepts(s) (if any) of the graphs of the given equations.

nd the x-intercept(s) and y-intercepts(s) (if any) of the graphs of the given equations.

nd the x-intercept(s) and y-intercepts(s) (if any) of the graphs of the given equations.

nd the x-intercept(s) and y-intercepts(s) (if any) of the graphs of the given equations.

match the graph with the corresponding symmetry. a. No symmetry b. Symmetry with respect to the x-axis c. Symmetry with respect to the y-axis d. Symmetry with respect to the origin e. Symmetry with respect to the x-axis, y-axis, and origin

match the graph with the corresponding symmetry. a. No symmetry b. Symmetry with respect to the x-axis c. Symmetry with respect to the y-axis d. Symmetry with respect to the origin e. Symmetry with respect to the x-axis, y-axis, and origin

match the graph with the corresponding symmetry. a. No symmetry b. Symmetry with respect to the x-axis c. Symmetry with respect to the y-axis d. Symmetry with respect to the origin e. Symmetry with respect to the x-axis, y-axis, and origin

match the graph with the corresponding symmetry. a. No symmetry b. Symmetry with respect to the x-axis c. Symmetry with respect to the y-axis d. Symmetry with respect to the origin e. Symmetry with respect to the x-axis, y-axis, and origin

match the graph with the corresponding symmetry. a. No symmetry b. Symmetry with respect to the x-axis c. Symmetry with respect to the y-axis d. Symmetry with respect to the origin e. Symmetry with respect to the x-axis, y-axis, and origin

match the graph with the corresponding symmetry. a. No symmetry b. Symmetry with respect to the x-axis c. Symmetry with respect to the y-axis d. Symmetry with respect to the origin e. Symmetry with respect to the x-axis, y-axis, and origin

a point that lies on a graph is given along with that graphs symmetry. State the other known points that must also lie on the graph.

a point that lies on a graph is given along with that graphs symmetry. State the other known points that must also lie on the graph.

a point that lies on a graph is given along with that graphs symmetry. State the other known points that must also lie on the graph.

a point that lies on a graph is given along with that graphs symmetry. State the other known points that must also lie on the graph.

a point that lies on a graph is given along with that graphs symmetry. State the other known points that must also lie on the graph.

a point that lies on a graph is given along with that graphs symmetry. State the other known points that must also lie on the graph.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

test algebraically to determine whether the equations graph is symmetric with respect to the x-axis, y-axis, or origin.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

plot the graph of the given equation.

Sprinkler. A sprinkler will water a grassy area in the shape of x2  y2  9. Apply symmetry to draw the watered area, assuming the sprinkler is located at the origin

Sprinkler. A sprinkler will water a grassy area in the shape of Apply symmetry to draw the watered area, assuming the sprinkler is located at the origin.

Electronic Signals: Radio Waves. The received power of an electromagnetic signal is a fraction of the power transmitted. The relationship is given by where R is the distance that the signal has traveled in meters. Plot the percentage of transmitted power that is received for R  100 m, 1 km, and 10,000 km.

Electronic Signals: Laser Beams. The wavelength  and the frequency f of a signal are related by the equation where c is the speed of light in a vacuum, c  3.0  108 meters per second. For the values,   0.001,   1, and   100 mm, plot the points corresponding to frequency, f. What do you notice about the relationship between frequency and wavelength? Note that the frequency will have units Hz  1/seconds.

Prot. The prot associated with making a particular product is given by the equation where y represents the prot in millions of dollars and x represents the number of thousands of units sold. (x  1 corresponds to 1000 units and y  1 corresponds to $1M.) Graph this equation and determine how many units must be sold to break even (prot  0). Determine the range of units sold that correspond to making a prot.

Prot. The prot associated with making a particular product is given by the equation where y represents the prot in millions of dollars and x represents the number of thousands of units sold. (x  1 corresponds to 1000 units and y  1 corresponds to $1M.) Graph this equation and determine how many units must be sold to break even (prot  0). Determine the range of units sold that correspond to making a prot.

Economics. The demand for an electronic device is modeled by where x is thousands of units demanded per day and p is the price (in dollars) per unit. a. Find the domain of the demand equation. Interpret your result. b. Plot the demand equation.

Economics. The demand for a new electronic game is modeled by where x is thousands of units demanded per day and p is the price (in dollars) per unit. a. Find the domain of the demand equation. Interpret your result. b. Plot the demand equation.

explain the mistake that is made. Graph the equation y  x2  1. This is incorrect. What mistake was made?

explain the mistake that is made. Test y  x2 for symmetry with respect to the y-axis. Solution: Replace x with x. y  (x)2 Simplify. y  x2 The resulting equation is not equivalent to the original equation; y  x2 is not symmetric with respect to the y-axis. This is incorrect. What mistake was made?

explain the mistake that is made. Test x  y for symmetry with respect to the y-axis. Solution: Replace y with y. x  y Simplify. x  y The resulting equation is equivalent to the original equation; x  y is symmetric with respect to the y-axis. This is incorrect. What mistake was made?

explain the mistake that is made. Use symmetry to help you graph x2  y  1. Solution: Replace x with x.( x)2  y  1 Simplify. x2  y  1 x2  y  1 is symmetric with respect to the x-axis. Determine points that lie on the graph in quadrant I. x y 5 5 5 5 yx 2  y  1( x, y) 1 0 (0, 1) 2 1 (1, 2) 5 2 (2, 5) Symmetry with respect to the x-axis implies that (0, 1), (1, 2), and (2, 5) are also points that lie on the graph. This is incorrect. What mistake was made?

determine whether each statement is true or false. If the point (a, b) lies on a graph that is symmetric about the x-axis, then the point (a, b) also must lie on the graph.

determine whether each statement is true or false. If the point (a, b) lies on a graph that is symmetric about the y-axis, then the point (a, b) also must lie on the graph.

determine whether each statement is true or false. If the point (a, b) lies on a graph that is symmetric about the x-axis, y-axis, and origin, then the points (a, b), (a, b), and (a, b) must also lie on the graph.

determine whether each statement is true or false.Two points are all that is needed to plot the graph of an equation.

Determine whether the graph of has any symmetry, where a, b, and c are real numbers.

Find the intercepts of y  (x  a)2  b2, where a and b are real numbers.

graph the equation using a graphing utility and state whether there is any symmetry. y  16.7x4  3.3x2  7.1

graph the equation using a graphing utility and state whether there is any symmetry. y  0.4x5  8.2x3  1.3x

graph the equation using a graphing utility and state whether there is any symmetry.2.3x2  5.5 y

graph the equation using a graphing utility and state whether there is any symmetry.3.2x2  5.1y2  1.3

graph the equation using a graphing utility and state whether there is any symmetry.1.2x2  4.7y2  19.4

graph the equation using a graphing utility and state whether there is any symmetry.2.1y2  0.8 x  1

nd the slope of the line that passes through the given points. (1, 3) and (2, 6)

nd the slope of the line that passes through the given points. (2, 1) and (4, 9)

nd the slope of the line that passes through the given points. (2, 5) and (2, 3)

nd the slope of the line that passes through the given points. (1, 4) and (4, 6)

nd the slope of the line that passes through the given points. (7, 9) and (3, 10)

nd the slope of the line that passes through the given points. (11, 3) and (2, 6)

nd the slope of the line that passes through the given points. (0.2, 1.7) and (3.1, 5.2)

nd the slope of the line that passes through the given points. (2.4, 1.7) and (5.6, 2.3)

nd the slope of the line that passes through the given points. .

nd the slope of the line that passes through the given points. A1 2, 3 5B and A-3 4, 7 5BA

identify (by inspection) the x- and y-intercepts and slope if they exist, and classify the line as rising, falling, horizontal, or vertical.

identify (by inspection) the x- and y-intercepts and slope if they exist, and classify the line as rising, falling, horizontal, or vertical.

identify (by inspection) the x- and y-intercepts and slope if they exist, and classify the line as rising, falling, horizontal, or vertical.

identify (by inspection) the x- and y-intercepts and slope if they exist, and classify the line as rising, falling, horizontal, or vertical.

identify (by inspection) the x- and y-intercepts and slope if they exist, and classify the line as rising, falling, horizontal, or vertical.

identify (by inspection) the x- and y-intercepts and slope if they exist, and classify the line as rising, falling, horizontal, or vertical.

nd the x- and y-intercepts if they exist and graph the corresponding line. y  2x  3

nd the x- and y-intercepts if they exist and graph the corresponding line. y 3x  2

nd the x- and y-intercepts if they exist and graph the corresponding line. . .

nd the x- and y-intercepts if they exist and graph the corresponding line.

nd the x- and y-intercepts if they exist and graph the corresponding line. 2x  3y  4

nd the x- and y-intercepts if they exist and graph the corresponding line. x  y  1

nd the x- and y-intercepts if they exist and graph the corresponding line.

nd the x- and y-intercepts if they exist and graph the corresponding line. 1 3 x - 1 4 y = 1 12

nd the x- and y-intercepts if they exist and graph the corresponding line. . x 1

nd the x- and y-intercepts if they exist and graph the corresponding line. y 3

nd the x- and y-intercepts if they exist and graph the corresponding line. y  1.5

nd the x- and y-intercepts if they exist and graph the corresponding line. x 7.5

nd the x- and y-intercepts if they exist and graph the corresponding line.

nd the x- and y-intercepts if they exist and graph the corresponding line.

write the equation in slopeintercept form. Identify the slope and the y-intercept.2x  5y  10

write the equation in slopeintercept form. Identify the slope and the y-intercept. 3x  4y  12

write the equation in slopeintercept form. Identify the slope and the y-intercept.x  3y  6

write the equation in slopeintercept form. Identify the slope and the y-intercept. x  2y  8

write the equation in slopeintercept form. Identify the slope and the y-intercept. 4x  y  3

write the equation in slopeintercept form. Identify the slope and the y-intercept. x  y  5

write the equation in slopeintercept form. Identify the slope and the y-intercept.12  6x  3y

write the equation in slopeintercept form. Identify the slope and the y-intercept.4  2x  8y

write the equation in slopeintercept form. Identify the slope and the y-intercept.0.2x  0.3y  0.6

write the equation in slopeintercept form. Identify the slope and the y-intercept.0.4x  0.1y  0.3

write the equation in slopeintercept form. Identify the slope and the y-intercept.

write the equation in slopeintercept form. Identify the slope and the y-intercept.

write the equation of the line, given the slope and intercept.

write the equation of the line, given the slope and intercept.

write the equation of the line, given the slope and intercept.

write the equation of the line, given the slope and intercept.

write the equation of the line, given the slope and intercept.

write the equation of the line, given the slope and intercept.

write the equation of the line, given the slope and intercept.

write the equation of the line, given the slope and intercept.

write an equation of the line in slopeintercept form, if possible, given the slope and a point that lies on the line.

write an equation of the line in slopeintercept form, if possible, given the slope and a point that lies on the line.

write an equation of the line in slopeintercept form, if possible, given the slope and a point that lies on the line.

write an equation of the line in slopeintercept form, if possible, given the slope and a point that lies on the line.

write an equation of the line in slopeintercept form, if possible, given the slope and a point that lies on the line.

write an equation of the line in slopeintercept form, if possible, given the slope and a point that lies on the line.

write an equation of the line in slopeintercept form, if possible, given the slope and a point that lies on the line.

write an equation of the line in slopeintercept form, if possible, given the slope and a point that lies on the line.

write an equation of the line in slopeintercept form, if possible, given the slope and a point that lies on the line.

write an equation of the line in slopeintercept form, if possible, given the slope and a point that lies on the line.

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (2, 1) and (3, 2)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (4, 3) and (5, 1)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (3, 1) and (2, 6)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (5, 8) and (7, 2)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (20, 37) and (10, 42)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (8, 12) and (20, 12)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (1, 4) and (2, 5)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. 2, 3) and (2, 3)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b.

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b.

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (3, 5) and (3, 7)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (5, 2) and (5, 4)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (3, 7) and (9, 7)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (2, 1) and (3, 1)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (0, 6) and (5, 0)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (0, 3) and (0, 2)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (6, 8) and (6, 2)

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b. (9, 0) and (9, 2

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b.

write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form x  a or y  b.

write the equation corresponding to each line. Express the equation in slopeintercept form.

write the equation corresponding to each line. Express the equation in slopeintercept form.

write the equation corresponding to each line. Express the equation in slopeintercept form.

write the equation corresponding to each line. Express the equation in slopeintercept form.

write the equation corresponding to each line. Express the equation in slopeintercept form.

write the equation corresponding to each line. Express the equation in slopeintercept form.

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. (3, 1); parallel to the line y  2x  1

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. (1, 3); parallel to the line y  x  2

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. (0, 0); perpendicular to the line 2x  3y  12

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. (0, 6); perpendicular to the line x  y  7

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. (3, 5); parallel to the x-axis

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. (3, 5); parallel to the y-axis

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. (1, 2); perpendicular to the y-axis

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. (1, 2); perpendicular to the x-axis

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. (2, 7); parallel to the line

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. (1, 4); perpendicular to the li

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. ; perpendicular to the line

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. perpendicular to the line

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. parallel to the line

nd the equation of the line that passes through the given point and also satises the additional piece of information. Express your answer in slopeintercept form, if possible. parallel to the line 10x + 45y =-9

Budget: Home Improvement. The cost of having your bathroom remodeled is the combination of material costs and labor costs. The materials (tile, grout, toilet, xtures, etc.) cost is $1200, and the labor cost is $25 per hour. Write an equation that models the total cost C of having your bathroom remodeled as a function of hours h. How much will the job cost if the worker estimates 32hours?

Budget: Rental Car. The cost of a one-day car rental is the sum of the rental fee, $50, plus $0.39 per mile. Write an equation that models the total cost associated with the car rental.

Budget: Monthly Driving Costs. The monthly costs associated with driving a new Honda Accord are the monthly loan payment plus $25 every time you ll up with gasoline. If you ll up 5 times in a month, your total monthly cost is $500. How much is your loan payment?

Budget: Monthly Driving Costs. The monthly costs associated with driving a Ford Explorer are the monthly loan payment plus the cost of lling up your tank with gasoline. If you ll up 3 times in a month, your total monthly cost is $520. If you ll up 5 times in a month, your total monthly cost is $600. How much is your monthly loan, and how much does it cost every time you ll up with gasoline?

Business. The operating costs for a local business are a xed amount of $1300 plus $3.50 per unit sold, while revenue is $7.25 per unit sold. How many units does the business have to sell in order to break even?

Business. The operating costs for a local business are a xed amount of $12,000 plus $13.50 per unit sold, while revenue is $27.25 per unit sold. How many units does the business have to sell in order to break even?

Weather: Temperature. The National Oceanic and Atmospheric Administration (NOAA) has an online conversion chart that relates degrees Fahrenheit, F, to degrees Celsius, C. 77F is equivalent to 25C, and 68F is equivalent to 20C. Assuming the relationship is linear, writethe equation relating degrees Celsius Cto degrees Fahrenheit F. What temperature is the same in both degrees Celsius and degrees Fahrenheit?

Weather: Temperature. According to NOAA, a standard day is 15C at sea level, and every 500 feet elevation above sea level corresponds to a 1C temperature drop. Assuming the relationship between temperature and elevation is linear, write an equation that models this relationship. What is the expected temperature at 2500 feet on a standard day?

Life Sciences: Height. The average height of a man has increased over the last century. What is the rate of change in inches per year of the average height of men?

Life Sciences: Height. The average height of a woman has increased over the last century. What is the rate of change in inches per year of the average height of women?

Life Sciences: Weight. The average weight of a baby born in 1900 was 6 pounds 4 ounces. In 2000, the average weight of a newborn was 6 pounds 10 ounces. What is the rate of change of birth weight in ounces per year? What do we expect babies to weigh at birth in 2040?

Sports. The fastest a man could run a mile in 1906 was 4 minutes and 30 seconds. In 1957, Don Bowden became the rst American to break the 4-minute mile. Calculate the rate of change in mile speed per year.

Monthly Phone Costs. Mikes home phone plan charges a at monthly fee plus a charge of $0.05 per minute for long-distance calls. The total monthly charge is represented by y  0.05x  35, x

Cost: Automobile. The value of a Daewoo car is given by y  11,100  1850x, x

Weather: Rainfall. The average rainfall in Norfolk, Virginia, for July was 5.2 inches in 2003. The average July rainfall for Norfolk was 3.8 inches in 2007. What is the rate of change of rainfall in inches per year? If this trend continues, what is the expected average rainfall in 2010?

Weather: Temperature. The average temperature for Boston in January 2005 was 43F. In 2007 the average January temperature was 44.5F. What is the rate of change of the temperature per year? If this trend continues, what is the expected average temperature in January 2010?

Environment. In 2000, Americans used approximately 380 billion plastic bags. In 2005, approximately 392 billion were used. What is the rate of change of plastic bags used per year? How many plastic bags will be expected to be used in 2010?

Finance: Debt. According to the Federal Reserve, Americans individually owed $744 in revolving credit in 2004. In 2006, they owed approximately $788. What is the rate of change of the amount of revolving credit owed per year? How much should Americans be expected to owe in 2008?

Business. A website that supplies Asian specialty foods to restaurants advertises a 64 ounce bottle of Hoisin Sauce for $16.00. Shipping cost for one bottle is $15.93. The shipping cost for two bottles is $19.18. The cost for ve bottles, including shipping, is $111.83. Answer the following questions based on this scenario. Round to the nearest cent, when necessary. a. Write the three ordered pairs where x represents the number of bottles purchased and y represents the total cost (including shipping) for one, two, or ve bottles purchased. b. Calculate the slope between the origin and the ordered pair that represents the purchase of one bottle of Hoisin Sauce. Explain what this amount means in terms of the sauce purchase. c. Calculate the slope between the origin and the ordered pair that represents the purchase of two bottles of Hoisin (including shipping). Explain what this amount means in terms of the sauce purchase. d. Calculate the slope between the origin and the ordered pair that represents the purchase of ve bottles of Hoisin (including shipping). Explain what this amount means in terms of the sauce purchase.

Business. A website that supplies Asian specialty foods to restaurants advertises an 8 ounce bottle of Plum Sauce for $4.00, but shipping for one bottle is $14.27. The shipping cost for two bottles is $14.77. The cost for ve bottles, including shipping, is $35.93. Answer the following questions based on this scenario. Round to the nearest cent, when necessary. a. Write the three ordered pairs where x represents the number of bottles purchased and y represents the total cost, including shipping for one, two, or ve bottles purchased. b. Calculate the slope between the origin and the ordered pair that represents the purchase of one bottle of Plum Sauce. Explain what this amount means in terms of the sauce purchase. c. Calculate the slope between the origin and the ordered pair that represents the purchase of two bottles of Plum Sauce (including shipping). Explain what this amount means in terms of the sauce purchase. d. Calculate the slope between the origin and the ordered pair that represents the purchase of ve bottles of Plum Sauce (including shipping). Explain what this amount means in terms of the sauce purchase.

explain the mistake that is made. Find the x- and y-intercepts of the line with equation 2x  3y  6. Solution: x-intercept: set x  0 and solve for y. 3y  6 y 2 The x-intercept is (0, 2). y-intercept: set y  0 and solve for x.2 x  6 x  3 The y-intercept is (3, 0). This is incorrect. What mistake was made?

explain the mistake that is made. Find the slope of the line that passes through the points (2, 3) and (4, 1). Solution: Write the slope formula. Substitute (2, 3) and (4, 1). This is incorrect. What mistake was made?

explain the mistake that is made. Find the slope of the line that passes through the points (3, 4) and (3, 7). Solution: Write the slope formula. Substitute (3, 4) and (3, 7). This is incorrect. What mistake was made?

explain the mistake that is made. Given the slope, classify the line as rising, falling, horizontal, or vertical. a. m  0 b. m undened c. m  2 d. m 1 Solution: a. vertical line b. horizontal line c. rising d. falling These are incorrect. What mistakes were made?

determine whether each statement is true or false. A line can have at most one x-intercept.

determine whether each statement is true or false. A line must have at least one y-intercept.

determine whether each statement is true or false. If the slopes of two lines are and 5, then the lines are parallel.

determine whether each statement is true or false. If the slopes of two lines are 1 and 1, then the lines are perpendicular.

If a line has slope equal to zero, describe a line that is perpendicular to it.

If a line has no slope, describe a line that is parallel to it.

Find an equation of a line that passes through the point (B, A  1) and is parallel to the line Ax  By  C. Assume that B is not equal to zero.

Find an equation of a line that passes through the point (B, A 1) and is parallel to the line Ax  By  C. Assume that B is not equal to zero.

Find an equation of a line that passes through the point (A, B 1) and is perpendicular to the line Ax  By  C. Assume that A and B are both nonzero.

Find an equation of a line that passes through the point (A, B  1) and is perpendicular to the line Ax  By  C. Assume that A and B are both nonzero.

Show that two lines with equal slopes and different y-intercepts have no point in common. Hint: Let y1  mx  b1 and y2  mx  b2 with . What equation must be true for there to be a point of intersection? Show that this leads to a contradiction.

Let y1  m1x  b1 and y2  m2x  b2 be two nonparallel lines . What is the x-coordinate of the point where they intersect?

determine whether the lines are parallel, perpendicular, or neither, and then graph both lines in the same viewing screen using a graphing utility to conrm your answer. y1  17x  22 y2 =1 17x - 13

determine whether the lines are parallel, perpendicular, or neither, and then graph both lines in the same viewing screen using a graphing utility to conrm your answer. y1  0.35x  2.7 y2  0.35x  1.2

determine whether the lines are parallel, perpendicular, or neither, and then graph both lines in the same viewing screen using a graphing utility to conrm your answer. y1  0.25x  3.3 y2 4x  2

determine whether the lines are parallel, perpendicular, or neither, and then graph both lines in the same viewing screen using a graphing utility to conrm your answer.

determine whether the lines are parallel, perpendicular, or neither, and then graph both lines in the same viewing screen using a graphing utility to conrm your answer. y1  0.16x  2.7 y2  6.25x  1.4

determine whether the lines are parallel, perpendicular, or neither, and then graph both lines in the same viewing screen using a graphing utility to conrm your answer. y1 3.75x  8.2 y2 = 4 15 x + 5 6

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

write the equation of the circle in standard form.

nd the center and radius of the circle with the given equations. (x  1)2  (y  3)2  25

nd the center and radius of the circle with the given equations. (x  1)2  (y  3)2  11

nd the center and radius of the circle with the given equations. (x  2)2  (y  5)2  49

nd the center and radius of the circle with the given equations. (x  3)2  (y  7)2  81

nd the center and radius of the circle with the given equations. (x  4)2  (y  9)2  20

nd the center and radius of the circle with the given equations. (x  1)2  (y  2)2  8

nd the center and radius of the circle with the given equations.

nd the center and radius of the circle with the given equations.

nd the center and radius of the circle with the given equations. (x  1.5)2  (y  2.7)2  1.69

nd the center and radius of the circle with the given equations. (x  3.1)2  (y  7.4)2  56.25

nd the center and radius of the circle with the given equations. x2  y2  50  0

nd the center and radius of the circle with the given equations. x2  y2  8  0

state the center and radius of each circle. x2  y2  4x  6y  3  0

state the center and radius of each circle. x2  y2  2x  10y  17  0

state the center and radius of each circle. x2  y2  6x  8y  75  0

state the center and radius of each circle. x2  y2  2x  4y  9  0

state the center and radius of each circle. x2  y2  10x  14y  7  0

state the center and radius of each circle. x2  y2  4x  16y  32  0

state the center and radius of each circle. x2  y2  2y  15  0

state the center and radius of each circle. x2  y2  2x  8  0

state the center and radius of each circle. x2  y2  2x  6y  1  0

state the center and radius of each circle. x2  y2  8x  6y  21  0

state the center and radius of each circle. x2  y2  10x  6y  22 

state the center and radius of each circle. x2  y2  8x  2y  28  0

state the center and radius of each circle. x2  y2  6x  4y  1  0

state the center and radius of each circle. x2  y2  2x  10y  2  0

state the center and radius of each circle. x2 + y2 x 2 3y 2 + 3 8 =

state the center and radius of each circle.

state the center and radius of each circle. x2  y2  2.6x  5.4y  1.26  0

state the center and radius of each circle. x2  y2  6.2x  8.4y  3  0

nd the equation of each circle. Centered at (1, 2) and passing through the point (1, 0).

nd the equation of each circle. Centered at (4, 9) and passing through the point (2, 5).

nd the equation of each circle. Centered at (2, 3) and passing through the point (3, 7).

nd the equation of each circle. Centered at (1, 1) and passing through the point (8, 5).

nd the equation of each circle. Centered at (2, 5) and passing through the point (1, 9).

nd the equation of each circle. Centered at (3, 4) and passing through the point (1, 8).

Cell Phones. If a cellular phone tower has a reception radius of 100 miles and you live 95 miles north and 33 miles east of the tower, can you use your cell phone while at home?

Cell Phones. Repeat Exercise 57, assuming you live 45 miles south and 87 miles west of the tower.

Construction/Home Improvement. A couple and their dog moved into a new house that does not have a fenced-in backyard. The backyard is square with dimensions 100 feet by 100 feet. If they put a stake in the center of the backyard with a long leash, write the equation of the circle that will map out the dogs outer perimeter.

Construction/Home Improvement. Repeat Exercise 59 except that the couple put in a pool and a garden and want to restrict the dog to quadrant I. What coordinates represent the center of the circle? What is the radius?

Design. A university designs its campus with a master plan of two concentric circles. All of the academic buildings are within the inner circle (so that students can get between classes in less than 10 minutes), and the outer circle contains all the dormitories, the Greek park, cafeterias, the gymnasium, and intramural elds. Assuming the center of campus is the origin, write an equation for the inner circle if the diameter is 3000 feet.

Design. Repeat Exercise 61 for the outer circle with a diameter of 6000 feet.

Cell Phones. A cellular phone tower has a reception radius of 200 miles. Assuming the tower is located at the origin, write the equation of the circle that represents the reception area.

Environment. In a state park, a re has spread in the form of a circle. If the radius is 2 miles, write an equation for the circle.

refer to the following: A cell phone provider is expanding its coverage and needs to place four cell phone towers to provide complete coverage of a 100-square-mile area formed by a 10 mile by 10 mile square. This area can be represented by a region on the Cartesian coordinate system; see gure. The placement of the four towers is very important in that the cell phone provider needs to provide coverage of the entire 100-square-mile area. The cell phone towers being installed can process signals from cell phones within a 3.5-mile radius. Engineering. One plan under consideration is to place the four towers in locations that correspond to the points (2.5, 2.5), (2.5, 7.5), (7.5, 2.5), and (7.5, 7.5) on the graph. a. Write an equation that describes the perimeter of the cell phone coverage for each of the four towers. b. Draw the coverage provided by each of these towers. Will this placement of towers provide the needed coverage?

refer to the following: A cell phone provider is expanding its coverage and needs to place four cell phone towers to provide complete coverage of a 100-square-mile area formed by a 10 mile by 10 mile square. This area can be represented by a region on the Cartesian coordinate system; see gure. The placement of the four towers is very important in that the cell phone provider needs to provide coverage of the entire 100-square-mile area. The cell phone towers being installed can process signals from cell phones within a 3.5-mile radius. Engineering. One plan under consideration is to place the four towers in locations that correspond to the points (3, 3), (3, 7), (7, 3), and (7, 7) on the graph. a. Write an equation that describes the perimeter of the cell phone coverage for each of the four towers. b. Draw the coverage provided by each of these towers. Will this placement of towers provide the needed coverage?

explain the mistake that is made.Identify the center and radius of the circle with equation (x  4)2  (y  3)2  25. Solution: The center is (4, 3) and the radius is 5. This is incorrect. What mistake was made?

explain the mistake that is made. Identify the center and radius of the circle with equation (x  2)2  (y  3)2  2. Solution: The center is (2, 3) and the radius is 2. This is incorrect. What mistake was made?

explain the mistake that is made. Graph the solution to the equation (x  1)2  (y  2)2 16. Solution: The center is (1, 2) and the radius is 4. This is incorrect. What mistake was made?

explain the mistake that is made. Find the center and radius of the circle with the equation x2  y2  6x  4y  3  0. Solution: Group like terms. (x2  6x)  (y2  4y)  3 Complete the (x2  6x  9)  (y2  4y  4)  12 square. The center is (3, 2) and the radius is . This is incorrect. What mistake was made?

determine whether each statement is true or false. The equation whose graph is depicted has innitely many solutions.

determine whether each statement is true or false. The equation (x  7)2  (y  15)2 64 has no solution.

determine whether each statement is true or false. The equation (x  2)2  (y  5)2 20 has no solution.

determine whether each statement is true or false. The equation (x  1)2  (y  3)2  0 has only one solution.

Describe the graph (if it exists) of: x2  y2  10x  6y  34  0

Describe the graph (if it exists) of: x2  y2  4x  6y  49  0

Find the equation of a circle that has a diameter with endpoints (5, 2) and (1, 6).

Find the equation of a circle that has a diameter with endpoints (3, 0) and (1, 4).

For the equation x2  y2  ax  by  c  0, specify conditions on a, b, and c so that the graph is a single point.

For the equation x2  y2  ax  by  c  0, specify conditions on a, b, and c so that there is no corresponding graph.

Determine the center and radius of the circle given by the equation x2  y2  2ax  100  a2.

Determine the center and radius of the circle given by the equation x2  y2  2by  49  b2.

use a graphing utility to graph each equation. Does this agree with the answer you gave in the Conceptual section? (x  2)2  (y  5)2 20 (See Exercise 73 for comparison.)

use a graphing utility to graph each equation. Does this agree with the answer you gave in the Conceptual section? (x  1)2  (y  3)2  0 (See Exercise 74 for comparison.)

use a graphing utility to graph each equation. Does this agree with the answer you gave in the Conceptual section? x2  y2  10x  6y  34  0 (See Exercise 75 for comparison.)

use a graphing utility to graph each equation. Does this agree with the answer you gave in the Conceptual section? x2  y2  4x  6y  49  0 (See Exercise 76 for comparison.)

(a) with the equation of the circle in standard form, state the center and radius, and graph; (b) use the quadratic formula to solve for y; and (c) use a graphing utility to graph each equation found in (b). Does the graph in (a) agree with the graphs in (c)? x2  y2 11x 3y 7.19 0

(a) with the equation of the circle in standard form, state the center and radius, and graph; (b) use the quadratic formula to solve for y; and (c) use a graphing utility to graph each equation found in (b). Does the graph in (a) agree with the graphs in (c)? x2  y2 1.2x 3.2y 2.11 0

for each of the following scatterplots, identify the pattern as a. having a positive association, negative association, or no identiable association. b. being linear or nonlinear.

for each of the following scatterplots, identify the pattern as a. having a positive association, negative association, or no identiable association. b. being linear or nonlinear.

for each of the following scatterplots, identify the pattern as a. having a positive association, negative association, or no identiable association. b. being linear or nonlinear.

for each of the following scatterplots, identify the pattern as a. having a positive association, negative association, or no identiable association. b. being linear or nonlinear.

match the following scatterplots with the following correlation coefcients. a. r 0.90 c. r 0.68 b. r  0.80 d. r  0.20

match the following scatterplots with the following correlation coefcients. a. r 0.90 c. r 0.68 b. r  0.80 d. r  0.20

match the following scatterplots with the following correlation coefcients. a. r 0.90 c. r 0.68 b. r  0.80 d. r  0.20

match the following scatterplots with the following correlation coefcients. a. r 0.90 c. r 0.68 b. r  0.80 d. r  0.20

For each of the following data sets, a. create a scatterplot. b. guess the value of the correlation coefcient r. c. use technology to determine the equation of the best t line and to calculate r. d. give a verbal description of the relationship between x and y.

For each of the following data sets, a. create a scatterplot. b. guess the value of the correlation coefcient r. c. use technology to determine the equation of the best t line and to calculate r. d. give a verbal description of the relationship between x and y.

For each of the following data sets, a. create a scatterplot. b. guess the value of the correlation coefcient r. c. use technology to determine the equation of the best t line and to calculate r. d. give a verbal description of the relationship between x and y.

For each of the following data sets, a. create a scatterplot. b. guess the value of the correlation coefcient r. c. use technology to determine the equation of the best t line and to calculate r. d. give a verbal description of the relationship between x and y.

For each of the following data sets, a. create a scatterplot. b. guess the value of the correlation coefcient r. c. use technology to determine the equation of the best t line and to calculate r. d. give a verbal description of the relationship between x and y.

For each of the following data sets, a. create a scatterplot. b. guess the value of the correlation coefcient r. c. use technology to determine the equation of the best t line and to calculate r. d. give a verbal description of the relationship between x and y.

for each of the data sets, a. use technology to create a scatterplot, to determine the best t line, and to compute r. b. indicate whether or not the best t line can be used for predictive purposes for the following x-values. For those for which it can be used, give the predicted value of y: i. x  0 iii. x  12 ii. x 6 iv. x 15 c. Using the best t line, at what x-value would you expect y to be equal to 2?

for each of the data sets, a. use technology to create a scatterplot, to determine the best t line, and to compute r. b. indicate whether or not the best t line can be used for predictive purposes for the following x-values. For those for which it can be used, give the predicted value of y: i. x  0 iii. x  12 ii. x 6 iv. x 15 c. Using the best t line, at what x-value would you expect y to be equal to 2?

for each of the data sets, a. use technology to create a scatterplot, to determine the best t line, and to compute r. b. indicate whether or not the best t line can be used for predictive purposes for the following x-values. For those for which it can be used, give the predicted value of y: i. x  0 iii. x  12 ii. x 6 iv. x 15 c. Using the best t line, at what x-value would you expect y to be equal to 2?

for each of the data sets, a. use technology to create a scatterplot, to determine the best t line, and to compute r. b. indicate whether or not the best t line can be used for predictive purposes for the following x-values. For those for which it can be used, give the predicted value of y: i. x  0 iii. x  12 ii. x 6 iv. x 15 c. Using the best t line, at what x-value would you expect y to be equal to 2?

a. use technology to create a scatterplot, to determine the best t line, and to compute r for the entire data set. b. repeat (a), but with the data set obtained by removing the starred (***) data points. c. compare the r-values from (a) and (b), as well as the slopes of the best t lines. Comment on any differences, whether they are substantive, and why this seems reasonable.

a. use technology to create a scatterplot, to determine the best t line, and to compute r for the entire data set. b. repeat (a), but with the data set obtained by removing the starred (***) data points. c. compare the r-values from (a) and (b), as well as the slopes of the best t lines. Comment on any differences, whether they are substantive, and why this seems reasonable.

a. use technology to create a scatterplot, to determine the best t line, and to compute r for the entire data set. b. repeat (a), but with the data set obtained by removing the starred (***) data points. c. compare the r-values from (a) and (b), as well as the slopes of the best t lines. Comment on any differences, whether they are substantive, and why this seems reasonable.

a. use technology to create a scatterplot, to determine the best t line, and to compute r for the entire data set. b. repeat (a), but with the data set obtained by removing the starred (***) data points. c. compare the r-values from (a) and (b), as well as the slopes of the best t lines. Comment on any differences, whether they are substantive, and why this seems reasonable.

Consider the data set from Exercise 17. a. Reverse the roles of xand yso that now yis the explanatory variable and x is the response variable. Create a scatterplot for the ordered pairs of the form (y, x) using this data set. b. Compute r. How does it compare to the r-value from Exercise 17? Why does this make sense? c. The best t line for the scatterplot in (a) will be of the form x  my  b. Determine this line. d. Using the line from (c), nd the predicted x-value for the following y-values, if appropriate. If it is not appropriate, tell why. i. y  23 ii. y  2 iii. y 16

Consider the data set from Exercise 16. Redo the parts in Exercise 23.

Consider the following data set.Guess the values of r and the best t line. Then, check your answers using technology. What happens? Can you reason why this is the case?

Consider the following data set. Guess the values of r and the best t line. Then, check your answers using technology. What happens? Can you reason why this is the case?

The following screenshot was taken when using the TI-83 to determine the equation of the best t line for paired data (x, y): Using the regression line, we observe that there is a strong positive linear association between x and y, and that for every unit increase in x, the y-value increases by about 1.257 units.

The following scatterplot was produced using the TI-83 for paired data (x, y). The equation of the best t line was reported to be y 3.207x  0.971 with r2  0.9827. Thus, the correlation coefcient is given by r  0.9913, which indicates a strong linear association between x and y.

refer to the data set in Example 1. a. Examine the relationship between each of the decathlon events and the total points by computing the correlation coefcient in each case. b. Using the information from part (a), which event has the strongest relationship to the total points? c. What is the equation of the best t line that describes the relationship between the event from part (b) and the total points? d. Using the best t line, if you had a score of 40 for this event, what would the predicted total points score be?

refer to the data set in Example 1. a. Using the information from part (a), which event has the second strongest relationship to the total points? b. What is the equation of the best t line that describes the relationship between the event in part (b) and the total points? c. Is it reasonable to expect the best t line from part (c) to produce accurate predictions of total points using this event? d. Using the best t line, if you had a score of 40 for this event, what would the total points score be?

refer to the following scenario: Texting Speed.According to the CTIAThe Wireless Association, as of December 2010, 187.7 billion messages were sent per month or 2.1 trillion messages in that year.1 According to a 2010 Pew Internet survey, 72% of all teensor 88% of teen cell phone usersare text-messagers. Teens make and receive far fewer phone calls than text messages on their cell phones. A number of competitions regarding texting speed have taken place worldwide. According to the Guinness World Records, The fastest completion of a prescribed 160-character text message is 34.65 seconds and was achieved by Frode Ness (Norway) at the Norwegian SMS championships held at the Oslo City shopping centre in Oslo, stlandet, Norway, on 13 November 2010.2 The data set regarding texting speed on the next page was provided by AP Central. (http://apcentral.collegeboard.com/apc/public/ courses/teachers_corner/195435.html) In the data given, the A total score is the amount of time (in seconds) it took to text the following message, Statistics students are above average. The B total score is the amount of time (in seconds) to type, Meet me at my car after school today. The Total both scores is the sum of the A total score and B total score. What inuences texting speed in this group? Lets consider thumb length. What is the relationship between the variables left thumb length and total both scores? a. Create a scatterplot to show the relationship between left thumb length and total both scores. b. What is the correlation coefcient between left thumb length and total both scores? c. Describe the strength of the relationship between left thumb length and total both scores. d. What is the equation of the best t line that describes the relationship between left thumb length and total both scores? e. Could you use the best t line to produce accurate predictions of total both scores using left thumb length

refer to the following scenario: Texting Speed.According to the CTIAThe Wireless Association, as of December 2010, 187.7 billion messages were sent per month or 2.1 trillion messages in that year.1 According to a 2010 Pew Internet survey, 72% of all teensor 88% of teen cell phone usersare text-messagers. Teens make and receive far fewer phone calls than text messages on their cell phones. A number of competitions regarding texting speed have taken place worldwide. According to the Guinness World Records, The fastest completion of a prescribed 160-character text message is 34.65 seconds and was achieved by Frode Ness (Norway) at the Norwegian SMS championships held at the Oslo City shopping centre in Oslo, stlandet, Norway, on 13 November 2010.2 The data set regarding texting speed on the next page was provided by AP Central. (http://apcentral.collegeboard.com/apc/public/ courses/teachers_corner/195435.html) In the data given, the A total score is the amount of time (in seconds) it took to text the following message, Statistics students are above average. The B total score is the amount of time (in seconds) to type, Meet me at my car after school today. The Total both scores is the sum of the A total score and B total score. What inuences texting speed in this group? Lets consider thumb length.Repeat Exercise 31 for right thumb length and total both scores.

refer to the following data set: Herd Immunity According to the U.S. Department of Health and Human Services, herd immunity is dened as a concept of protecting a community against certain diseases by having a high percentage of the communitys population immunized. Even if a few members of the community are unable to be immunized, the entire community will be indirectly protected because the disease has little opportunity for an outbreak. However, with a low percentage of population immunity, the disease would have great opportunity for an outbreak.3 Suppose a study is conducted in the year 2016 looking at the outbreak of Haemophilus inuenzae type b in the winter of 2015 across 22 nursing homes. We might look at the percentage of residents in each of the nursing homes that were immunized and the percentage of residents who were infected with this type of inuenza. The ctional data set is as follows. What is the relationship between the variables % residents immunized and % residents with inuenza? a. Create a scatterplot to illustrate the relationship between % residents immunized and % residents with inuenza. b. What is the correlation coefcient between % residents immunized and % residents with inuenza? c. Describe the strength of the relationship between % residents immunized and % residents with inuenza. d. What is the equation of the best t line that describes the relationship between % residents immunized and % residents with inuenza? e. Could you use the best t line to produce accurate predictions of % residents with inuenza using % residents immunized?

refer to the following data set: Herd Immunity According to the U.S. Department of Health and Human Services, herd immunity is dened as a concept of protecting a community against certain diseases by having a high percentage of the communitys population immunized. Even if a few members of the community are unable to be immunized, the entire community will be indirectly protected because the disease has little opportunity for an outbreak. However, with a low percentage of population immunity, the disease would have great opportunity for an outbreak.3 Suppose a study is conducted in the year 2016 looking at the outbreak of Haemophilus inuenzae type b in the winter of 2015 across 22 nursing homes. We might look at the percentage of residents in each of the nursing homes that were immunized and the percentage of residents who were infected with this type of inuenza. The ctional data set is as follows. What is the impact of the outlier(s) on this data set? a. Identify the outlier in this data set. What is the nursing home number for this outlier? b. Remove the outlier and re-create the scatterplot to show the relationship between % residents immunized and % residents with inuenza. c. What is the revised correlation coefcient between % residents immunized and % residents with inuenza? d. By removing the outlier is the strength of the relationship between % residents immunized and % residents with inuenza increased or decreased? e. What is the revised equation of the best t line that describes the relationship between % residents immunized and % residents with inuenza?

refer to the following data set: Amusement Park Rides. According to the International Association of Amusement Parks and Attractions (IAAPA), There are more than 400 amusement parks and traditional attractions in the United States alone. In 2008, amusement parks in the United States entertained 300 million visitors who safely enjoyed more than 1.7 billion rides.4 Despite the popularity of amusement parks, the wait times, especially for the most popular rides, are not so highly regarded. There are different approaches and tactics that people take to get the most rides in their visit to the park. Now, there are even apps for the iPhone and Android to track waiting times at various amusement parks. One might ask, Are the wait times worth it? Are the rides with the longest wait times, the most enjoyable? Consider the following ctional data. The data shows 10 popular rides in two sister parks located in Florida and California. For each ride in each park, average wait times (in minutes) in the summer of 2010 and the average rating of ride enjoyment (on a scale of 1100) are provided. What is the relationship between the variables average wait times and average rating of enjoyment? a. Create a scatterplot to show the relationship between average wait times and average rating of enjoyment. b. What is the correlation coefcient between average wait times and average rating of enjoyment? c. Describe the strength of the relationship between average wait times and average rating of enjoyment. d. What is the equation of the best t line that describes the relationship between average wait times and average rating of enjoyment? e. Could you use the best t line to produce accurate predictions of average wait times using average rating of enjoyment?

refer to the following data set: Amusement Park Rides. According to the International Association of Amusement Parks and Attractions (IAAPA), There are more than 400 amusement parks and traditional attractions in the United States alone. In 2008, amusement parks in the United States entertained 300 million visitors who safely enjoyed more than 1.7 billion rides.4 Despite the popularity of amusement parks, the wait times, especially for the most popular rides, are not so highly regarded. There are different approaches and tactics that people take to get the most rides in their visit to the park. Now, there are even apps for the iPhone and Android to track waiting times at various amusement parks. One might ask, Are the wait times worth it? Are the rides with the longest wait times, the most enjoyable? Consider the following ctional data. The data shows 10 popular rides in two sister parks located in Florida and California. For each ride in each park, average wait times (in minutes) in the summer of 2010 and the average rating of ride enjoyment (on a scale of 1100) are provided. Examine the relationship between average wait times and average rating of enjoyment for Park 1 in Florida by repeating Exercise 35 for only Park 1.

refer to the following data set: Amusement Park Rides. According to the International Association of Amusement Parks and Attractions (IAAPA), There are more than 400 amusement parks and traditional attractions in the United States alone. In 2008, amusement parks in the United States entertained 300 million visitors who safely enjoyed more than 1.7 billion rides.4 Despite the popularity of amusement parks, the wait times, especially for the most popular rides, are not so highly regarded. There are different approaches and tactics that people take to get the most rides in their visit to the park. Now, there are even apps for the iPhone and Android to track waiting times at various amusement parks. One might ask, Are the wait times worth it? Are the rides with the longest wait times, the most enjoyable? Consider the following ctional data. The data shows 10 popular rides in two sister parks located in Florida and California. For each ride in each park, average wait times (in minutes) in the summer of 2010 and the average rating of ride enjoyment (on a scale of 1100) are provided. Examine the relationship between average wait times and average rating of enjoyment for Park 2 in California repeating Exercise 35 for only Park 2.

refer to the following data set: Amusement Park Rides. According to the International Association of Amusement Parks and Attractions (IAAPA), There are more than 400 amusement parks and traditional attractions in the United States alone. In 2008, amusement parks in the United States entertained 300 million visitors who safely enjoyed more than 1.7 billion rides.4 Despite the popularity of amusement parks, the wait times, especially for the most popular rides, are not so highly regarded. There are different approaches and tactics that people take to get the most rides in their visit to the park. Now, there are even apps for the iPhone and Android to track waiting times at various amusement parks. One might ask, Are the wait times worth it? Are the rides with the longest wait times, the most enjoyable? Consider the following ctional data. The data shows 10 popular rides in two sister parks located in Florida and California. For each ride in each park, average wait times (in minutes) in the summer of 2010 and the average rating of ride enjoyment (on a scale of 1100) are provided. Compare the relationship between average wait times and average rating of enjoyment for Park 1 in Florida versus Park 2 in California.

refer to the following: Exploring other types of best-t curves When describing the patterns that emerge in paired data sets, there are many more possibilities other than best t lines. Indeed, once you have drawn a scatterplot and are ready to identify the curve that best ts the data, there is a substantive collection of other curves that might more accurately describe the data. The following are listed among those in STATS/CALC on the TI-83, along with some comments eate a scatterplot. b. Use LinReg(axb) to determine the best t line and r. Does the line seem to accurately describe the pattern in the data? c. For each of the different choices listed in the above chart, nd the equation of the best t curve and its associated r2 value. Of all of the curves, which seems to provide the best t? Note: The r2-value reported in each case is NOT the linear correlation coefcient reported when running LinReg(axB). Rather, the value will typically change depending on the curve. The reason why is that each time, the r2-value is measuring how accurate the t is between the data and that type of curve. A value of r2 close to 1 still corresponds to a good t with whichever curve you are tting to the data.

refer to the following: Exploring other types of best-t curves When describing the patterns that emerge in paired data sets, there are many more possibilities other than best t lines. Indeed, once you have drawn a scatterplot and are ready to identify the curve that best ts the data, there is a substantive collection of other curves that might more accurately describe the data. The following are listed among those in STATS/CALC on the TI-83, along with some comments eate a scatterplot. b. Use LinReg(axb) to determine the best t line and r. Does the line seem to accurately describe the pattern in the data? c. For each of the different choices listed in the above chart, nd the equation of the best t curve and its associated r2 value. Of all of the curves, which seems to provide the best t? Note: The r2-value reported in each case is NOT the linear correlation coefcient reported when running LinReg(axB). Rather, the value will typically change depending on the curve. The reason why is that each time, the r2-value is measuring how accurate the t is between the data and that type of curve. A value of r2 close to 1 still corresponds to a good t with whichever curve you are tting to the data.

refer to the following: Exploring other types of best-t curves When describing the patterns that emerge in paired data sets, there are many more possibilities other than best t lines. Indeed, once you have drawn a scatterplot and are ready to identify the curve that best ts the data, there is a substantive collection of other curves that might more accurately describe the data. The following are listed among those in STATS/CALC on the TI-83, along with some comments eate a scatterplot. b. Use LinReg(axb) to determine the best t line and r. Does the line seem to accurately describe the pattern in the data? c. For each of the different choices listed in the above chart, nd the equation of the best t curve and its associated r2 value. Of all of the curves, which seems to provide the best t? Note: The r2-value reported in each case is NOT the linear correlation coefcient reported when running LinReg(axB). Rather, the value will typically change depending on the curve. The reason why is that each time, the r2-value is measuring how accurate the t is between the data and that type of curve. A value of r2 close to 1 still corresponds to a good t with whichever curve you are tting to the data.

refer to the following: Exploring other types of best-t curves When describing the patterns that emerge in paired data sets, there are many more possibilities other than best t lines. Indeed, once you have drawn a scatterplot and are ready to identify the curve that best ts the data, there is a substantive collection of other curves that might more accurately describe the data. The following are listed among those in STATS/CALC on the TI-83, along with some comments eate a scatterplot. b. Use LinReg(axb) to determine the best t line and r. Does the line seem to accurately describe the pattern in the data? c. For each of the different choices listed in the above chart, nd the equation of the best t curve and its associated r2 value. Of all of the curves, which seems to provide the best t? Note: The r2-value reported in each case is NOT the linear correlation coefcient reported when running LinReg(axB). Rather, the value will typically change depending on the curve. The reason why is that each time, the r2-value is measuring how accurate the t is between the data and that type of curve. A value of r2 close to 1 still corresponds to a good t with whichever curve you are tting to the data.

Plot each point and indicate which quadrant the point lies in. (4, 2)

Plot each point and indicate which quadrant the point lies in. (4, 7)

Plot each point and indicate which quadrant the point lies in. (1, 6)

Plot each point and indicate which quadrant the point lies in. (2, 1)

Calculate the distance between the two points. (2, 0) and (4, 3)

Calculate the distance between the two points. (1, 4) and (4, 4)

Calculate the distance between the two points. (4, 6) and (2, 7)

Calculate the distance between the two points. and

Calculate the midpoint of the segment joining the two points. . (2, 4) and (3, 8)

Calculate the midpoint of the segment joining the two points. (2, 6) and (5, 7)

Calculate the midpoint of the segment joining the two points. (2.3, 3.4) and (5.4, 7.2)

Calculate the midpoint of the segment joining the two points. (a, 2) and (a, 4)

Sports.A quarterback drops back to pass. At the point (5, 20) he throws the ball to his wide receiver located at (10, 30). Find the distance the ball has traveled. Assume the width of the football eld is [15, 15] and the length is [50, 50]. Units of measure are yards.

Sports. Suppose that in the above exercise a defender was midway between the quarterback and the receiver. At what point was the defender located when the ball was thrown over his head?

Find the x-intercept(s) and y-intercept(s) if any. x2  4y2  4

Find the x-intercept(s) and y-intercept(s) if any. y  x2  x  2

Find the x-intercept(s) and y-intercept(s) if any. y = 2x2 - 9

Find the x-intercept(s) and y-intercept(s) if any. y = x2 - x - 12 x - 12

Use algebraic tests to determine symmetry with respect to the x-axis, y-axis, or origin. x2  y3  4

Use algebraic tests to determine symmetry with respect to the x-axis, y-axis, or origin. y  x2  2

Use algebraic tests to determine symmetry with respect to the x-axis, y-axis, or origin. xy  4

Use algebraic tests to determine symmetry with respect to the x-axis, y-axis, or origin. y2  5  x

Use symmetry as a graphing aid and point-plot the given equations. y  x2  3

Use symmetry as a graphing aid and point-plot the given equations. y  x  4

Use symmetry as a graphing aid and point-plot the given equations. y = 3

Use symmetry as a graphing aid and point-plot the given equations. x  y2  2

Use symmetry as a graphing aid and point-plot the given equations. y = x29 - x2

Use symmetry as a graphing aid and point-plot the given equations. x2  y2  36

Sports.A track around a high school football eld is in the shape of the graph 8x2  y2  8. Graph using symmetry and by plotting points.

Transportation. A bypass around a town follows the graph y  x3  2, where the origin is the center of town. Graph the equation.

Express the equation for each line in slopeintercept form. Identify the slope and y-intercept of each line. 6x  2y  12

Express the equation for each line in slopeintercept form. Identify the slope and y-intercept of each line. 3x  4y  9

Express the equation for each line in slopeintercept form. Identify the slope and y-intercept of each line. -1 2x - 1 3y = 1 6

Express the equation for each line in slopeintercept form. Identify the slope and y-intercept of each line. -2 3x - 1 4y = 1 8

Find the x- and y-intercepts and the slope of each line if they exist and graph. y  4x  5

Find the x- and y-intercepts and the slope of each line if they exist and graph. y =3 4x - 3

Find the x- and y-intercepts and the slope of each line if they exist and graph. x  y  4

Find the x- and y-intercepts and the slope of each line if they exist and graph. x 4

Find the x- and y-intercepts and the slope of each line if they exist and graph. y  2

Find the x- and y-intercepts and the slope of each line if they exist and graph. -1 2x - 1 2y = 3

Write the equation of the line, given the slope and the intercepts. Slope: m  4 y-intercept: (0, 3)

Write the equation of the line, given the slope and the intercepts. Slope: m  0 y-intercept: (0, 4)

Write the equation of the line, given the slope and the intercepts. Slope: m is undened x-intercept: (3, 0)

Write the equation of the line, given the slope and the intercepts. Slope: y-intercept

Write an equation of the line, given the slope and a point that lies on the line. m 2( 3, 4)

Write an equation of the line, given the slope and a point that lies on the line. (2, 16)

Write an equation of the line, given the slope and a point that lies on the line. m  0( 4, 6)

Write an equation of the line, given the slope and a point that lies on the line. m is undened (2, 5)

Write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form of x  a or y  b. (4, 2) and (2, 3)

Write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form of x  a or y  b. (1, 4) and (2, 5)

Write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form of x  a or y  b. A-3 4, 1 2B and A-7 4, 5 2B

Write the equation of the line that passes through the given points. Express the equation in slopeintercept form or in the form of x  a or y  b. (3, 2) and (9, 2)

Find the equation of the line that passes through the given point and also satises the additional piece of information.(2, 1) parallel to the line 2x  3y  6

Find the equation of the line that passes through the given point and also satises the additional piece of information. (5, 6) perpendicular to the line 5x  3y  0

Find the equation of the line that passes through the given point and also satises the additional piece of information. perpendicular to the line

Find the equation of the line that passes through the given point and also satises the additional piece of information. (a  2, b  1) parallel to the line Ax  By  C

Grades. For a GRE prep class, a student must take a pretest and then a posttest after the completion of the course. Two students results are shown below. Give a linear equation to represent the given data.

Budget: Car Repair. The cost of having the air conditioner in your car repaired is the combination of material costs and labor costs. The materials (tubing, coolant, etc.) are $250, and the labor costs $38 per hour. Write an equation that models the total cost C of having your air conditioner repaired as a function of hours t. Graph this equation with t as the horizontal axis and C representing the vertical axis. How much will the job cost if the mechanic works 1.5 hours?

Write the equation of the circle in standard form. center (2, 3) r  6

Write the equation of the circle in standard form. center (6, 8)

Write the equation of the circle in standard form. center A3 4, 5 2B

Write the equation of the circle in standard form. . center (1.2, 2.4) r  3.6

Find the center and the radius of the circle given by the equation. (x  2)2  (y  3)2  81

Find the center and the radius of the circle given by the equation. (x  4)2  (y  2)2  32

Find the center and the radius of the circle given by the equation. Ax + 3 4B2 + Ay - 1 2B2 = 16 36

Find the center and the radius of the circle given by the equation. x2  y2  4x  2y  0

Find the center and the radius of the circle given by the equation. x2  y2  2y  4x  11  0

Find the center and the radius of the circle given by the equation. 3x2  3y2  6x  7  0

Find the center and the radius of the circle given by the equation. 9x2  9y2  6x  12y  76 

Find the center and the radius of the circle given by the equation. x2  y2  3.2x  6.6y  2.4  0

Find the center and the radius of the circle given by the equation. Find the equation of a circle centered at (2, 7) and passing through (3, 6).

Find the center and the radius of the circle given by the equation. Find the equation of a circle that has the diameter with endpoints (2, 1) and (5, 5).

Determine whether the triangle with the given vertices is a right triangle, isosceles triangle, neither, or both. (10, 5), (20, 45), (10, 10)

Determine whether the triangle with the given vertices is a right triangle, isosceles triangle, neither, or both. (4.2, 8.4), (4.2, 2.1), (6.3, 10.5)

Graph the equation using a graphing utility and state whether there is any symmetry. y2 = x2 - 4

Graph the equation using a graphing utility and state whether there is any symmetry. 0.8x2 - 1.5y2 = 4.8

Determine whether the lines are parallel, perpendicular, or neither, then graph both lines in the same viewing screen using a graphing utility to conrm your answer.

Determine whether the lines are parallel, perpendicular, or neither, then graph both lines in the same viewing screen using a graphing utility to conrm your answer.

Use the Quadratic Formula to solve for y, and use a graphing utility to graph each equation. Do the graphs agree with the graph in Exercise 69?

Use the Quadratic Formula to solve for y, and use a graphing utility to graph each equation. Do the graphs agree with the graph in Exercise 70?

Find the distance between the points (7, 3) and (2, 2).

Find the midpoint between (3, 5) and (5, 1).

Determine the length and the midpoint of a segment that joins the points (2, 4) and (3, 6).

Research Triangle. The Research Triangle in North Carolina was established as a collaborative research center among Duke University (Durham), North Carolina State University (Raleigh), and the University of North Carolina (Chapel Hill) Durham is 10 miles north and 8 miles east of Chapel Hill, and Raleigh is 28 miles east and 15 miles south of Chapel Hill. What is the perimeter of the research triangle? Round your answer to the nearest mile.

Determine the two values for y so that the point (3, y) is 5 units away from the point (6, 5).

If the point (3, 4) is on a graph that is symmetric with respect to the y-axis, what point must also be on the graph?

Determine whether the graph of the equation x  y2  5 has any symmetry (x-axis, y-axis, and origin).

Find the x-intercept(s) and the y-intercept(s), if any: 4x2  9y2  36.

Graph the following equations.2x2  y2  8

Graph the following equations. = 4 x2 + 1

Graph the following equations. Find the x-intercept and the y-intercept of the line x  3y  6.

Express the line in slopeintercept form: 4x  6y  12.

Express the line in slopeintercept form: .

Find the equation of the line that is characterized by the given information. Graph the line. Slope  4; y-intercept (0, 3)

Find the equation of the line that is characterized by the given information. Graph the line. Passes through the points (3, 2) and (4, 9)

Find the equation of the line that is characterized by the given information. Graph the line. Parallel to the line y  4x  3 and passes through the point (1, 7)

Find the equation of the line that is characterized by the given information. Graph the line. Perpendicular to the line 2x  4y  5 and passes through the point (1, 1)

Find the equation of the line that is characterized by the given information. Graph the line. x-intercept (3, 0); y-intercept (0, 6)

write the equation of the line that corresponds to the graph.

write the equation of the line that corresponds to the graph.

Write the equation of a circle that has center (6, 7) and radius r  8.

Determine the center and radius of the circle x2  y2  10x  6y  22  0.

Find the equation of the circle that is centered at (4, 9) and passes through the point (2, 5).

Solar System. Earth is approximately 93 million miles from the Sun. Approximating Earths orbit around the Sun as circular, write an equation governing Earths path around the Sun. Locate the Sun at the origin.

Determine whether the triangle with the given vertices is a right triangle, isosceles triangle, neither, or both.

Graph the given equation using a graphing utility and state whether there is any symmetry. 0.25y2 + 0.04x2 = 1

Simplify .

Simplify and express in terms of positive exponents:

Perform the operation and simplify: (x  4)2 (x  4)2.

Factor completely 8x3  27y3.

Perform the operations and simplify:

Solve for x: x3  5x2  4x  20  0.

Perform the operations and write in standard form:

Solve for x. 15  [5  3x  4(2x  6)]  4(6x  7)  [5(3x  7)  6x  10]

Solve for x. 5 4x + 1 = 3 4x - 1

Ashley inherited $17,000. She invested some money in a CD that earns 5% and the rest in a stock that earns 8%. How much was invested in each account, if the interest for the rst year is $1075?

Solve by factoring: 5x2  45.

Solve by completing the square: 3x2  6x  7.

Use the discriminant to determine the number and type of roots: 5x2  2x  7  0.

Solve for r: p2  q2  r2.

Solve and check: . 2x2 +

Solve using substitution: .

Solve and express the solution in interval notation: 6 6 1 4x + 6 6 9

Solve and express the solution in interval notation: x2  x 20

Solve and express the solution in interval notation: 2  x 4

Solve and express the solution in interval notation: Solve for x: 5  4x  23.

Solve and express the solution in interval notation: Use algebraic tests to determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, or origin.

Solve and express the solution in interval notation: Write an equation of a line in slopeintercept form with slope that passes through the point (5, 1).

Solve and express the solution in interval notation: Write an equation of a line that is perpendicular to the x-axis and passes through the point (5, 3).

Solve and express the solution in interval notation: Write an equation of a line in slopeintercept form that passes through the two points

Solve and express the solution in interval notation: Find the center and radius of the circle: (x  5)2  (y  3)2  30.

Solve and express the solution in interval notation: Calculate the distance between the two points and nd the midpoint of the segment joining the two points. Round your answers to one decimal place.

Solve and express the solution in interval notation: Determine whether the lines and y1 = 0.32x + 1.5 are parallel, perpendicular, or neither, then graph both lines in the same viewing screen using a graphing utility to conrm your answer.