Precalculus with Limits : A Graphing Approach

Ron Larson, Robert Hostetler, Bruce H. Edwards

Chapter 1

Functions and Their Graphs - all with Video Answers

Educators

Section 1

Lines in the Plane

Problem 1

Identify the line that has the indicated slope.
(a) $m=\frac{2}{3}$ $\qquad$ (b) $m$ is undefined. $\qquad$ (c) $m=-2$

Amy Jiang

Amy Jiang

Numerade Educator

Problem 2

Identify the line that has the indicated slope.
(a) $m=0 \qquad$ (b) $m=-\frac{3}{4} \qquad$ (c) $m=1$

Mukesh Devi

Numerade Educator

Problem 3

Sketch the lines through the point with the indicated slopes on the same set of coordinate axes.
$(2,3)$ (a) 0 $\quad$ (b) 1 $\quad$ (c) 2 $\quad$ (d) $-3$

Amy Jiang

Numerade Educator

Problem 4

Sketch the lines through the point with the indicated slopes on the same set of coordinate axes.
$(-4,1)$ (a) 3 $\quad$ (b) $-3$ $\quad$ (c) $\frac{1}{2}$ $\quad$ (d) Undefined

Amy Jiang

Numerade Educator

Problem 5

Estimate the slope of the line.

Amy Jiang

Numerade Educator

Problem 6

Estimate the slope of the line.

Amy Jiang

Numerade Educator

Problem 7

Find the slope of the line passing through the pair of points. Then use a graphing utility to plot the points and use the draw feature to graph the line segment connecting the two points. (Use a square setting.)
$(0,-10),(-4,0)$

Amy Jiang

Numerade Educator

Problem 8

Find the slope of the line passing through the pair of points. Then use a graphing utility to plot the points and use the draw feature to graph the line segment connecting the two points. (Use a square setting.)
$(2,4),(4,-4)$

Amy Jiang

Numerade Educator

Problem 9

Find the slope of the line passing through the pair of points. Then use a graphing utility to plot the points and use the draw feature to graph the line segment connecting the two points. (Use a square setting.)
$(-6,-1),(-6,4)$

Amy Jiang

Numerade Educator

Problem 10

Find the slope of the line passing through the pair of points. Then use a graphing utility to plot the points and use the draw feature to graph the line segment connecting the two points. (Use a square setting.)
$(-3,-2),(1,6)$

Amy Jiang

Numerade Educator

Problem 11

Use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)
Point$\quad$ Slope
$(2,1) \quad m=0$

Amy Jiang

Numerade Educator

Problem 12

Use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)
Point$\quad$ Slope
$(3,-2) \quad m=0$

Amy Jiang

Numerade Educator

Problem 13

Use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)
Point$\quad$ Slope
$(1,5) \quad m$ is undefined

Amy Jiang

Numerade Educator

Problem 14

Use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)
Point$\quad$ Slope
$(-4,1) \quad m$ is undefined.

Amy Jiang

Numerade Educator

Problem 15

Use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)
Point$\quad$ Slope
$(0,-9) \quad m=-2$

Amy Jiang

Numerade Educator

Problem 16

Use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)
Point$\quad$ Slope
$(-5,4) \quad m=2$

Amy Jiang

Numerade Educator

Problem 17

Use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)
Point$\quad$ Slope
$(7,-2) \quad m=\frac{1}{2}$

Amy Jiang

Numerade Educator

Problem 18

Use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)
Point$\quad$ Slope
$(-1,-6) \quad m=-\frac{1}{2}$

Amy Jiang

Numerade Educator

Problem 19

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b).
$5 x-y+3=0$

Amy Jiang

Numerade Educator

Problem 20

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b).
$2 x+3 y-9=0$

Amy Jiang

Numerade Educator

Problem 21

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b).
$5 x-2=0$

Amy Jiang

Numerade Educator

Problem 22

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b).
$3 x+7=0$

Amy Jiang

Numerade Educator

Problem 23

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b).
$3 y+5=0$

Amy Jiang

Numerade Educator

Problem 24

(a) find the slope and y-intercept (if possible) of the equation of the line algebraically, and (b) sketch the line by hand. Use a graphing utility to verify your answers to parts (a) and (b).
$-11-8 y=0$

Amy Jiang

Numerade Educator

Problem 25

Find the general form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible.
Point $\quad$ Slope
$(0,-2) \quad m=3$

Amy Jiang

Numerade Educator

Problem 26

Find the general form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible.
Point $\quad$ Slope
$(-3,6) \quad m=-2$

Amy Jiang

Numerade Educator

Problem 27

Find the general form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible.
Point $\quad$ Slope
$(2,-3) \quad m=-\frac{1}{2}$

Amy Jiang

Numerade Educator

Problem 28

Find the general form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible.
Point $\quad$ Slope
$(-2,-5) \quad m=\frac{3}{4}$

Amy Jiang

Numerade Educator

Problem 29

Find the general form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible.
Point $\quad$ Slope
$(6,-1) \quad m$ is undefined.

Amy Jiang

Numerade Educator

Problem 30

Find the general form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible.
Point $\quad$ Slope
$(-10,4) \quad m$ is undefined.

Amy Jiang

Numerade Educator

Problem 31

Find the general form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible.
Point $\quad$ Slope
$\left(-\frac{1}{2}, \frac{3}{2}\right) \quad m=0$

Amy Jiang

Numerade Educator

Problem 32

Find the general form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible.
Point $\quad$ Slope
$(2.3,-8.5) \quad m=0$

Amy Jiang

Numerade Educator

Problem 33

Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line.
$(5,-1),(-5,5)$

Amy Jiang

Numerade Educator

Problem 34

Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line.
$(4,3),(-4,-4)$

Amy Jiang

Numerade Educator

Problem 35

Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line.
$(-8,1),(-8,7)$

Amy Jiang

Numerade Educator

Problem 36

Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line.
$(-1,4),(6,4)$

Amy Jiang

Numerade Educator

Problem 37

Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line.
$\left(2, \frac{1}{2}\right),\left(\frac{1}{2}, \frac{5}{4}\right)$

Amy Jiang

Numerade Educator

Problem 38

Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line.
$(1,1),\left(6,-\frac{2}{3}\right)$

Amy Jiang

Numerade Educator

Problem 39

Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line.
$\left(-\frac{1}{10},-\frac{3}{5}\right),\left(\frac{9}{10},-\frac{9}{5}\right)$

Amy Jiang

Numerade Educator

Problem 40

Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line.
$\left(\frac{3}{4}, \frac{3}{2}\right),\left(-\frac{4}{3}, \frac{7}{4}\right)$

Amy Jiang

Numerade Educator

Problem 41

Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line.
$(1,0.6),(-2,-0.6)$

Amy Jiang

Numerade Educator

Problem 42

Find the slope-intercept form of the equation of the line that passes through the points. Use a graphing utility to graph the line.
$(-8,0.6),(2,-2.4)$

Amy Jiang

Numerade Educator

Problem 43

Find the slope-intercept form of the equation of the line shown.

Amy Jiang

Numerade Educator

Problem 44

Find the slope-intercept form of the equation of the line shown.

Amy Jiang

Numerade Educator

Problem 45

Annual Salary A jeweler's salary was $\$ 28,500$ in 2004 and $\$ 32,900$ in 2006 . The jeweler's salary follows a linear growth pattern. What will the jeweler's salary be in 2008$?$

Amy Jiang

Numerade Educator

Problem 46

Annual Salary A librarian's salary was $\$ 25,000$ in 2004 and $\$ 27,500$ in 2006 . The librarian's salary follows a linear growth pattern. What will the librarian's salary be in 2008$?$

Amy Jiang

Numerade Educator

Problem 47

Determine the slope and $y$-intercept of the linear equation. Then describe its graph.
$x-2 y=4$

Amy Jiang

Numerade Educator

Problem 48

Determine the slope and $y$-intercept of the linear equation. Then describe its graph.
$3 x+4 y=1$

Amy Jiang

Numerade Educator

Problem 49

Determine the slope and $y$-intercept of the linear equation. Then describe its graph.
$x=-6$

Amy Jiang

Numerade Educator

Problem 50

Determine the slope and $y$-intercept of the linear equation. Then describe its graph.
$y=12$

Amy Jiang

Numerade Educator

Problem 51

Use a graphing utility to graph the equation using each of the suggested viewing windows. Describe the difference between the two graphs.
$y=0.5 x-3$
$\begin{array}{l}{\mathrm{Xmin}=-5} \\ {\mathrm{Xmax}=10} \\ {\mathrm{Xscl}=1} \\ {\mathrm{Ymin}=-1} \\ {\mathrm{Ymax}=10} \\ {\mathrm{Yscl}=1}\end{array}$ $\begin{array}{l}{\mathrm{Xmin}=-2} \\ {\mathrm{Xmax}=10} \\ {\mathrm{Xscl}=1} \\ {\mathrm{Ymin}=-4} \\ {\mathrm{Ymax}=1} \\ {\mathrm{Yscl}=1}\end{array}$

Amy Jiang

Numerade Educator

Problem 52

Use a graphing utility to graph the equation using each of the suggested viewing windows. Describe the difference between the two graphs.
$y=-8 x+5$
$\begin{array}{l}{\mathrm{Xmin}=-5} \\ {\mathrm{Xmax}=5} \\ {\mathrm{Xscl}=1} \\ {\mathrm{Ymin}=-10} \\ {\mathrm{Ymax}=10} \\ {\mathrm{Yscl}=1}\end{array}$ $\begin{array}{l}{\mathrm{Xmin}=-5} \\ {\mathrm{Xmax}=10} \\ {\mathrm{Xscl}=1} \\ {\mathrm{Ymin}=-80} \\ {\mathrm{Ymax}=80} \\ {\mathrm{Yscl}=20}\end{array}$

Amy Jiang

Numerade Educator

Problem 53

Determine whether the lines and passing through the pairs of points are parallel, perpendicular, or neither.
$L_{1} :(0,-1),(5,9)$
$L_{2} :(0,3),(4,1)$

Amy Jiang

Numerade Educator

Problem 54

Determine whether the lines and passing through the pairs of points are parallel, perpendicular, or neither.
$L_{1} :(-2,-1),(1,5)$
$L_{2} :(1,3),(5,-5)$

Amy Jiang

Numerade Educator

Problem 55

Determine whether the lines and passing through the pairs of points are parallel, perpendicular, or neither.
$L_{1} :(3,6),(-6,0)$
$L_{2} :(0,-1),\left(5, \frac{7}{3}\right)$

Amy Jiang

Numerade Educator

Problem 56

Determine whether the lines and passing through the pairs of points are parallel, perpendicular, or neither.
$L_{1} :(4,8),(-4,2)$
$L_{2} :(3,-5),\left(-1, \frac{1}{3}\right)$

Amy Jiang

Numerade Educator

Problem 57

Write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.
Point $\quad$ Line
$(2,1) \quad 4 x-2 y=3$

Amy Jiang

Numerade Educator

Problem 58

Write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.
Point $\quad$ Line
$(-3,2) \quad x+y=7$

Amy Jiang

Numerade Educator

Problem 59

Write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.
Point $\quad$ Line
$\left(-\frac{2}{3}, \frac{7}{8}\right) \quad 3 x+4 y=7$

Amy Jiang

Numerade Educator

Problem 60

Write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.
Point $\quad$ Line
$(-3.9,-1.4) \quad 6 x+2 y=9$

Amy Jiang

Numerade Educator

Problem 61

Write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.
Point $\quad$ Line
$(3,-2) \quad x-4=0$

Amy Jiang

Numerade Educator

Problem 62

Write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line.
Point $\quad$ Line
$(-4,1) \quad y+2=0$

Amy Jiang

Numerade Educator

Problem 63

The lines are parallel. Find the slope-intercept form of the equation of line $y_{2} .$

Amy Jiang

Numerade Educator

Problem 64

The lines are parallel. Find the slope-intercept form of the equation of line $y_{2} .$

Amy Jiang

Numerade Educator

Problem 65

The lines are perpendicular. Find the slope-intercept form of the equation of line $y_{2} .$

Amy Jiang

Numerade Educator

Problem 66

The lines are perpendicular. Find the slope-intercept form of the equation of line $y_{2} .$

Amy Jiang

Numerade Educator

Problem 67

Identify any relationships that exist among the lines, and then use a graphing utility to graph the three equations in the same viewing window. Adjust the viewing window so that each slope appears visually correct. Use the slopes of the lines to verify your results.
(a) $y=2 x \quad$ (b) $y=-2 x\quad$ (c) $y=\frac{1}{2} x$

Amy Jiang

Numerade Educator

Problem 68

Identify any relationships that exist among the lines, and then use a graphing utility to graph the three equations in the same viewing window. Adjust the viewing window so that each slope appears visually correct. Use the slopes of the lines to verify your results.
(a) $y=\frac{2}{3} x \quad$ (b) $y=-\frac{3}{2} x \quad$ (c) $y=\frac{2}{3} x+2$

Amy Jiang

Numerade Educator

Problem 69

Identify any relationships that exist among the lines, and then use a graphing utility to graph the three equations in the same viewing window. Adjust the viewing window so that each slope appears visually correct. Use the slopes of the lines to verify your results.
(a) $y=-\frac{1}{2} x \quad$ (b) $y=-\frac{1}{2} x+3 \quad$ (c) $y=2 x-4$

Amy Jiang

Numerade Educator

Problem 70

Identify any relationships that exist among the lines, and then use a graphing utility to graph the three equations in the same viewing window. Adjust the viewing window so that each slope appears visually correct. Use the slopes of the lines to verify your results.
(a) $y=x-8 \quad$ (b) $y=x+1 \quad$ (c) $y=-x+3$

Amy Jiang

Numerade Educator

Problem 71

The graph shows the earnings per share of stock for Circuit City for the years 1995 through 2004.
(a) Use the slopes to determine the years in which the earnings per share of stock showed the greatest increase and greatest decrease.
(b) Find the equation of the line between the years 1995 and 2004.
(c) Interpret the meaning of the slope of the equation from part (b) in the context of the problem.
(d) Use the equation from part (b) to estimate the earnings per share of stock in the year 2010. Do you think this is an accurate estimation? Explain.

Linda Hand

Numerade Educator

Problem 72

The graph shows the sales (in billions of dollars) for Goodyear Tire for the years 1995 through 2004, where $t=5$ represents 1995.
(a) Use the slopes to determine the years in which the sales
for Goodyear Tire showed the greatest increase and the smallest increase.
(b) Find the equation of the line between the years 1995 and 2004.
(c) Interpret the meaning of the slope of the equation from part (b) in the context of the problem.
(d) Use the equation from part (b) to estimate the sales for Goodyear Tire in the year 2010. Do you think this is an accurate estimation? Explain.

Linda Hand

Numerade Educator

Problem 73

The “rise to run” ratio of the roof of a house determines the steepness of the roof. The rise to run ratio of the roof in the figure is 3 to 4. Determine the maximum height in the attic of the house if the house is 32 feet wide.

Linda Hand

Numerade Educator

Problem 74

When driving down a mountain road, you notice warning signs indicating that it is a "12\% grade." This means that the slope of the road is $-\frac{12}{100}$ . Approximate the amount of horizontal change in your position if you note from elevation markers that you have descended 2000 feet vertically.

Amy Jiang

Numerade Educator

Problem 75

You are given the dollar value of a product in 2006 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let represent 2006.)
2006 Value $\quad$ Rate
$\$ 2540 \quad \$ 125$ increase per year

Amy Jiang

Numerade Educator

Problem 76

You are given the dollar value of a product in 2006 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let represent 2006.)
2006 Value $\quad$ Rate
$\$ 156 \quad \$ 4.50$ increase per year

Amy Jiang

Numerade Educator

Problem 77

You are given the dollar value of a product in 2006 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let represent 2006.)
2006 Value $\quad$ Rate
$\$ 20,400 \quad \$ 2000$ decrease per year

Amy Jiang

Numerade Educator

Problem 78

You are given the dollar value of a product in 2006 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let represent 2006.)
2006 Value $\quad$ Rate
$\$ 245,000 \quad \$ 5600$ decrease per year

Amy Jiang

Numerade Educator

Problem 79

Match the description with its graph. Determine the slope of each graph and how it is interpreted in the given context. [The graphs are labeled (a), (b), (c), and (d).]
You are paying $\$ 10$ per week to repay a $\$ 100$ loan.

Amy Jiang

Numerade Educator

Problem 80

Match the description with its graph. Determine the slope of each graph and how it is interpreted in the given context. [The graphs are labeled (a), (b), (c), and (d).]
An employee is paid $\$ 12.50$ per hour plus $\$ 1.50$ for each unit produced per hour.

Linda Hand

Numerade Educator

Problem 81

Match the description with its graph. Determine the slope of each graph and how it is interpreted in the given context. [The graphs are labeled (a), (b), (c), and (d).]
A sales representative receives $\$ 30$ per day for food plus $\$ .35$ for each mile traveled.

Linda Hand

Numerade Educator

Problem 82

Match the description with its graph. Determine the slope of each graph and how it is interpreted in the given context. [The graphs are labeled (a), (b), (c), and (d).]
A computer that was purchased for $\$ 600$ depreciates $\$ 100$ per year.

Linda Hand

Numerade Educator

Problem 83

Match the description with its graph. Determine the slope of each graph and how it is interpreted in the given context. [The graphs are labeled (a), (b), (c), and (d).]
A school district purchases a high-volume printer, copier, and scanner for $\$ 25,000$ . After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $\$ 2000$.
(a) Write a linear equation giving the value $V$ of the equipment during the 10 years it will be used.
(b) Use a graphing utility to graph the linear equation representing the depreciation of the equipment, and use the value or trace feature to complete the table.
$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline t & {0} & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {9} & {10} \\ \hline V & {} & {} & {} & {} & {} & {} & {} & {} & {} & {} \\ \hline\end{array}$
(c) Verify your answers in part (b) algebraically by using the equation you found in part (a).

Linda Hand

Numerade Educator

Problem 84

Meteorology Recall that water freezes at $0^{\circ} \mathrm{C}\left(32^{\circ} \mathrm{F}\right)$ and boils at $100^{\circ} \mathrm{C}\left(212^{\circ} \mathrm{F}\right) .$
(a) Find an equation of the line that shows the relationship between the temperature in degrees Celsius and degrees Fahrenheit $F$
(b) Use the result of part (a) to complete the table.
$\begin{array}{|c|c|c|c|c|c|}\hline C & {} & {-10^{\circ}} & {10^{\circ}} & {} & {} & {177^{\circ}} \\ \hline F & {0^{\circ}} & {} & {} & {68^{\circ}} & {90^{\circ}} & {} \\ \hline\end{array}$

Linda Hand

Numerade Educator

Problem 85

A contractor purchases a bulldozer for $\$ 36,500$ . The bulldozer requires an average expenditure of $\$ 5.25$ per hour for fuel and maintenance, and the operator is paid $\$ 11.50$ per hour.
(a) Write a linear equation giving the total cost $C$ of operating the bulldozer for $t$ hours. (Include the purchase cost of the bulldozer.)
(b) Assuming that customers are charged $\$ 27$ per hour of bulldozer use, write an equation for the revenue $R$ derived from $t$ hours of use.
(c) Use the profit formula $(P=R-C)$ to write an equation for the profit derived from $t$ hours of use.
(d) Use the result of part (c) to find the break-even point (the number of hours the bulldozer must be used to yield a profit of 0 dollars).

Linda Hand

Numerade Educator

Problem 86

A real estate office handles an apartment complex with 50 units. When the rent per unit is $\$ 580$ per month, all 50 units are occupied. However, when the rent is $\$ 625$ per month, the average number of occupied units drops to $47 .$ Assume that the relationship between the monthly rent $p$ and the demand $x$ is linear.
(a) Write the equation of the line giving the demand $x$ in terms of the rent $p$ .
(b) Use a graphing utility to graph the demand equation and use the trace feature to estimate the number of units occupied when the rent is $\$ 655 .$ Verify your answer algebraically.
(c) Use the demand equation to predict the number of units occupied when the rent is lowered to $\$ 595 .$ Verify your answer graphically.

Linda Hand

Numerade Educator

Problem 87

In 1991, Penn State University had an enrollment of 75,349 students. By 2005, the enrollment had increased to 80,124.
(a) What was the average annual change in enrollment from 1991 to 2005?
(b) Use the average annual change in enrollment to estimate the enrollments in 1984, 1997, and 2000.
(c) Write the equation of a line that represents the given data. What is its slope? Interpret the slope in the context of the problem.

Linda Hand

Numerade Educator

Problem 88

Using the results of Exercise 87, write a short paragraph discussing the concepts of slope and average rate of change.

Jerelyn Nevil

Numerade Educator

Problem 89

Determine whether the statement is true or false. Justify your answer.
The line through $(-8,2)$ and $(-1,4)$ and the line through $(0,-4)$ and $(-7,7)$ are parallel.

Amy Jiang

Numerade Educator

Problem 90

Determine whether the statement is true or false. Justify your answer.
If the points $(10,-3)$ and $(2,-9)$ lie on the same line, then the point $\left(-12,-\frac{37}{2}\right)$ also lies on that line.

Amy Jiang

Numerade Educator

Problem 91

Use a graphing utility to graph the equation of the line in the form
$\frac{x}{a}+\frac{y}{b}=1, \quad a \neq 0, b \neq 0$.
Use the graphs to make a conjecture about what a and b represent. Verify your conjecture.
$\frac{x}{5}+\frac{y}{-3}=1$

Amy Jiang

Numerade Educator

Problem 92

Use a graphing utility to graph the equation of the line in the form
$\frac{x}{a}+\frac{y}{b}=1, \quad a \neq 0, b \neq 0$.
Use the graphs to make a conjecture about what a and b represent. Verify your conjecture.
$\frac{x}{-6}+\frac{y}{2}=1$

Amy Jiang

Numerade Educator

Problem 93

Use a graphing utility to graph the equation of the line in the form
$\frac{x}{a}+\frac{y}{b}=1, \quad a \neq 0, b \neq 0$.
Use the graphs to make a conjecture about what a and b represent. Verify your conjecture.
$\frac{x}{4}+\frac{y}{-\frac{2}{3}}=1$

Amy Jiang

Numerade Educator

Problem 94

Use a graphing utility to graph the equation of the line in the form
$\frac{x}{a}+\frac{y}{b}=1, \quad a \neq 0, b \neq 0$.
Use the graphs to make a conjecture about what a and b represent. Verify your conjecture.
$\frac{x}{\frac{1}{2}}+\frac{y}{5}=1$

Amy Jiang

Numerade Educator

Problem 95

Use the results of Exercises 91–94 to write an equation of the line that passes through the points.
$x$ -intercept: $(2,0)$
$y$-intercept: $(0,3)$

Amy Jiang

Numerade Educator

Problem 96

Use the results of Exercises 91–94 to write an equation of the line that passes through the points.
$x$ -intercept: $(-5,0)$
$y$-intercept: $(0,-4)$

Amy Jiang

Numerade Educator

Problem 97

Use the results of Exercises 91–94 to write an equation of the line that passes through the points.
$x$-intercept: $\left(-\frac{1}{6}, 0\right)$
$y$-intercept: $\left(0,-\frac{2}{3}\right)$

Amy Jiang

Numerade Educator

Problem 98

Use the results of Exercises 91–94 to write an equation of the line that passes through the points.
$x$ -intercept: $\left(\frac{3}{4}, 0\right)$
$y$-intercept: $\left(0, \frac{4}{5}\right)$

Amy Jiang

Numerade Educator

Problem 99

Determine which equation(s) may be represented by the graph shown. (There may be more than one correct answer.)
(a) $2 x-y=-10$
(b) $2 x+y=10$
(c) $x-2 y=10$
(d) $x+2 y=10$

Amy Jiang

Numerade Educator

Problem 100

Determine which equation(s) may be represented by the graph shown. (There may be more than one correct answer.)
(a) $2 x+y=5$
(b) $2 x+y=-5$
(c) $x-2 y=5$
(d) $x-2 y=-5$

Amy Jiang

Numerade Educator

Problem 101

Determine which pair of equations may be represented by the graphs shown.
a) $2 x-y=5$
$2 x-y=1$
b) $2 x+y=-5$
$2 x+y=1$
c) $2 x-y=-5$
$2 x-y=1$
d) $x-2 y=-5$
$x-2 y=-1$

Linda Hand

Numerade Educator

Problem 102

Determine which pair of equations may be represented by the graphs shown.
a) $2 x-y=2$
$x+2 y=12$
b) $x-y=1$
$x+y=6$
c) $2 x+y=2$
$x-2 y=12$
d) $x-2 y=2$
$x+2 y=12$

Linda Hand

Numerade Educator

Problem 103

Does every line have both an x-intercept and a y-intercept? Explain.

Amy Jiang

Numerade Educator

Problem 104

Can every line be written in slope-intercept form? Explain.

Amy Jiang

Numerade Educator

Problem 105

Does every line have an infinite number of lines that are parallel to the given line? Explain.

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 106

Does every line have an infinite number of lines that are perpendicular to the given line? Explain.

Amy Jiang

Numerade Educator

Problem 107

Determine whether the expression is a polynomial. If it is, write the polynomial in standard form.
$x+20$

Amy Jiang

Numerade Educator

Problem 108

Determine whether the expression is a polynomial. If it is, write the polynomial in standard form.
$3 x-10 x^{2}+1$

Amy Jiang

Numerade Educator

Problem 109

Determine whether the expression is a polynomial. If it is, write the polynomial in standard form.
$4 x^{2}+x^{-1}-3$

Amy Jiang

Numerade Educator

Problem 110

Determine whether the expression is a polynomial. If it is, write the polynomial in standard form.
$2 x^{2}-2 x^{4}-x^{3}+2$

Amy Jiang

Numerade Educator

Problem 111

Determine whether the expression is a polynomial. If it is, write the polynomial in standard form.
$\frac{x^{2}+3 x+4}{x^{2}-9}$

Amy Jiang

Numerade Educator

Problem 112

Determine whether the expression is a polynomial. If it is, write the polynomial in standard form.
$\sqrt{x^{2}+7 x+6}$

Amy Jiang

Numerade Educator

Problem 113

Factor the trinomial.
$x^{2}-6 x-27$

Amy Jiang

Numerade Educator

Problem 114

Factor the trinomial.
$x^{2}-11 x+28$

Amy Jiang

Numerade Educator

Problem 115

Factor the trinomial.
$2 x^{2}+11 x-40$

Amy Jiang

Numerade Educator

Problem 116

Factor the trinomial.
$3 x^{2}-16 x+5$

Griffin Goodwin

Griffin Goodwin

Numerade Educator

Problem 117

To work an extended application analyzing the numbers of bachelor’s degrees earned by women in the United States from 1985 to 2005, visit this textbook’s Online Study Center.

John Johnson

Numerade Educator