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  • Algebra for College Students
  • Linear Equations and Inequalities in Two Variables

Algebra for College Students

Mark Dugopolski

Chapter 3

Linear Equations and Inequalities in Two Variables - all with Video Answers

Educators

Section 1

Graphing Lines in the Coordinate Plane

00:21

Problem 1

After reading this section, write out the answers to these questions. Use complete sentences.
What is the point called at the intersection of the $x$ -and $y$ -axis?

Heather Z.
Heather Z.
Numerade Educator
00:33

Problem 2

After reading this section, write out the answers to these questions. Use complete sentences.
What is an ordered pair?

Heather Z.
Heather Z.
Numerade Educator
01:00

Problem 3

After reading this section, write out the answers to these questions. Use complete sentences.
What are the $x$ - and $y$ -intercepts?

Heather Z.
Heather Z.
Numerade Educator
00:39

Problem 4

After reading this section, write out the answers to these questions. Use complete sentences.
What type of equation has a graph that is a horizontal line?

Heather Z.
Heather Z.
Numerade Educator
00:40

Problem 5

After reading this section, write out the answers to these questions. Use complete sentences.
What type of equation has a graph that is a vertical line?

Heather Z.
Heather Z.
Numerade Educator
00:20

Problem 6

After reading this section, write out the answers to these questions. Use complete sentences.
Which variable usually goes on the vertical axis?

Heather Z.
Heather Z.
Numerade Educator
00:23

Problem 7

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$(2,5)$$

Heather Z.
Heather Z.
Numerade Educator
00:25

Problem 8

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$(-5,1)$$

Heather Z.
Heather Z.
Numerade Educator
00:35

Problem 9

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$\left(-3,-\frac{1}{2}\right)$$

Heather Z.
Heather Z.
Numerade Educator
00:32

Problem 10

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$(-2,-6)$$

Heather Z.
Heather Z.
Numerade Educator
00:31

Problem 11

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$(0,4)$$

Heather Z.
Heather Z.
Numerade Educator
00:35

Problem 12

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$(0,2)$$

Heather Z.
Heather Z.
Numerade Educator
00:47

Problem 13

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$(\pi,-1)$$

Heather Z.
Heather Z.
Numerade Educator
00:34

Problem 14

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$\left(\frac{4}{3}, 0\right)$$

Heather Z.
Heather Z.
Numerade Educator
00:33

Problem 15

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$(-4,3)$$

Heather Z.
Heather Z.
Numerade Educator
00:30

Problem 16

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$(0,-3)$$

Heather Z.
Heather Z.
Numerade Educator
00:31

Problem 17

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$\left(\frac{3}{2}, 0\right)$$

Heather Z.
Heather Z.
Numerade Educator
00:33

Problem 18

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$(3,2)$$

Heather Z.
Heather Z.
Numerade Educator
00:35

Problem 19

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$\left(0,-\frac{7}{3}\right)$$

Heather Z.
Heather Z.
Numerade Educator
00:37

Problem 20

Plot the following points in a rectangular coordinate system. For each point, name the quadrant in which it lies or the axis on which it lies.
$$\left(4,-\frac{10}{3}\right)$$

Heather Z.
Heather Z.
Numerade Educator
00:47

Problem 21

Graph each linear equation. Plot four points for each line.
$$y=x+1$$

Heather Z.
Heather Z.
Numerade Educator
00:45

Problem 22

Graph each linear equation. Plot four points for each line.
$$y=x-1$$

Heather Z.
Heather Z.
Numerade Educator
00:51

Problem 23

Graph each linear equation. Plot four points for each line.
$$y=-2 x+3$$

Heather Z.
Heather Z.
Numerade Educator
00:49

Problem 24

Graph each linear equation. Plot four points for each line.
$$y=2 x-3$$

Heather Z.
Heather Z.
Numerade Educator
00:34

Problem 25

Graph each linear equation. Plot four points for each line.
$$y=x$$

Heather Z.
Heather Z.
Numerade Educator
00:38

Problem 26

Graph each linear equation. Plot four points for each line.
$$y=-x$$

Heather Z.
Heather Z.
Numerade Educator
00:37

Problem 27

Graph each linear equation. Plot four points for each line.
$$y=3$$

Heather Z.
Heather Z.
Numerade Educator
00:42

Problem 28

Graph each linear equation. Plot four points for each line.
$$y=-2$$

Heather Z.
Heather Z.
Numerade Educator
00:39

Problem 29

Graph each linear equation. Plot four points for each line.
$$y=1-x$$

Heather Z.
Heather Z.
Numerade Educator
00:38

Problem 30

Graph each linear equation. Plot four points for each line.
$$y=2-x$$

Heather Z.
Heather Z.
Numerade Educator
00:37

Problem 31

Graph each linear equation. Plot four points for each line.
$$x=2$$

Heather Z.
Heather Z.
Numerade Educator
00:39

Problem 32

Graph each linear equation. Plot four points for each line.
$$x=-3$$

Heather Z.
Heather Z.
Numerade Educator
00:55

Problem 33

Graph each linear equation. Plot four points for each line.
$$y=\frac{1}{2} x-1$$

Heather Z.
Heather Z.
Numerade Educator
00:51

Problem 34

Graph each linear equation. Plot four points for each line.
$$y=\frac{1}{3} x-2$$

Heather Z.
Heather Z.
Numerade Educator
00:46

Problem 35

Graph each linear equation. Plot four points for each line.
$$y+3=0$$

Heather Z.
Heather Z.
Numerade Educator
00:45

Problem 36

Graph each linear equation. Plot four points for each line.
$$y+4=0$$

Heather Z.
Heather Z.
Numerade Educator
00:43

Problem 37

Graph each linear equation. Plot four points for each line.
$$x-4=0$$

Heather Z.
Heather Z.
Numerade Educator
00:48

Problem 38

Graph each linear equation. Plot four points for each line.
$$x+5=0$$

Heather Z.
Heather Z.
Numerade Educator
00:44

Problem 39

Graph each linear equation. Plot four points for each line.
$$y=\frac{1}{2} x$$

Heather Z.
Heather Z.
Numerade Educator
01:12

Problem 40

Graph each linear equation. Plot four points for each line.
$$y=-\frac{2}{3} x$$

Heather Z.
Heather Z.
Numerade Educator
01:32

Problem 41

Graph each linear equation. Plot four points for each line.
$$3 x+y=5$$

Heather Z.
Heather Z.
Numerade Educator
01:17

Problem 42

Graph each linear equation. Plot four points for each line.
$$x+2 y=4$$

Heather Z.
Heather Z.
Numerade Educator
01:21

Problem 43

Graph each linear equation. Plot four points for each line.
$$6 x+3 y=0$$

Heather Z.
Heather Z.
Numerade Educator
01:29

Problem 44

Graph each linear equation. Plot four points for each line.
$$2 x+4 y=0$$

Heather Z.
Heather Z.
Numerade Educator
01:13

Problem 45

Graph each linear equation. Plot four points for each line.
$$y=2 x-20$$

Heather Z.
Heather Z.
Numerade Educator
01:00

Problem 46

Graph each linear equation. Plot four points for each line.
$$y=40-2 x$$

Heather Z.
Heather Z.
Numerade Educator
00:57

Problem 47

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$4 x-3 y=12$$

Heather Z.
Heather Z.
Numerade Educator
00:59

Problem 48

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$2 x+5 y=20$$

Heather Z.
Heather Z.
Numerade Educator
01:06

Problem 49

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$x-y+5=0$$

Heather Z.
Heather Z.
Numerade Educator
00:58

Problem 50

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$x+y+7=0$$

Heather Z.
Heather Z.
Numerade Educator
01:08

Problem 51

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$2 x+3 y=5$$

Heather Z.
Heather Z.
Numerade Educator
01:11

Problem 52

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$3 x-4 y=7$$

Heather Z.
Heather Z.
Numerade Educator
01:03

Problem 53

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$2 x-3 y=60$$

Heather Z.
Heather Z.
Numerade Educator
01:01

Problem 54

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$2 x+3 y=30$$

Heather Z.
Heather Z.
Numerade Educator
00:51

Problem 55

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$y=2 x-4$$

Heather Z.
Heather Z.
Numerade Educator
00:59

Problem 56

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$y=-3 x+6$$

Heather Z.
Heather Z.
Numerade Educator
01:04

Problem 57

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$y=-\frac{1}{2} x-20$$

Heather Z.
Heather Z.
Numerade Educator
01:08

Problem 58

Find the $x$ - and $y$ -intercepts for each line and use them to graph the line.
$$y=\frac{1}{3} x+10$$

Heather Z.
Heather Z.
Numerade Educator
01:59

Problem 59

Graph each equation on a graphing calculator using a window that shows both intercepts. Then use the appropriate feature of your calculator to find the intercepts.
$$y=-3 x+1$$

Heather Z.
Heather Z.
Numerade Educator
01:37

Problem 60

Graph each equation on a graphing calculator using a window that shows both intercepts. Then use the appropriate feature of your calculator to find the intercepts.
$$y=2-3 x$$

Heather Z.
Heather Z.
Numerade Educator
01:34

Problem 61

Graph each equation on a graphing calculator using a window that shows both intercepts. Then use the appropriate feature of your calculator to find the intercepts.
$$y=400 x-2$$

Heather Z.
Heather Z.
Numerade Educator
01:36

Problem 62

Graph each equation on a graphing calculator using a window that shows both intercepts. Then use the appropriate feature of your calculator to find the intercepts.
$$y=800 x+8$$

Heather Z.
Heather Z.
Numerade Educator
01:49

Problem 63

Graph each equation on a graphing calculator using a window that shows both intercepts. Then use the appropriate feature of your calculator to find the intercepts.
$$x+2 y=600$$

Heather Z.
Heather Z.
Numerade Educator
01:59

Problem 64

Graph each equation on a graphing calculator using a window that shows both intercepts. Then use the appropriate feature of your calculator to find the intercepts.
$$3 x-2 y=1500$$

Heather Z.
Heather Z.
Numerade Educator
01:50

Problem 65

Graph each equation on a graphing calculator using a window that shows both intercepts. Then use the appropriate feature of your calculator to find the intercepts.
$$y=4.26 x+23.54$$

Heather Z.
Heather Z.
Numerade Educator
01:42

Problem 66

Graph each equation on a graphing calculator using a window that shows both intercepts. Then use the appropriate feature of your calculator to find the intercepts.
$$y=30.6-3.6 x$$

Heather Z.
Heather Z.
Numerade Educator
00:43

Problem 67

Find all intercepts for each line. Some of these lines have only one intercept.
$$x+y=50$$

Heather Z.
Heather Z.
Numerade Educator
00:48

Problem 68

Find all intercepts for each line. Some of these lines have only one intercept.
$$x+2 y=100$$

Heather Z.
Heather Z.
Numerade Educator
00:53

Problem 69

Find all intercepts for each line. Some of these lines have only one intercept.
$$3 x-5 y=15$$

Heather Z.
Heather Z.
Numerade Educator
00:50

Problem 70

Find all intercepts for each line. Some of these lines have only one intercept.
$$9 x+8 y=72$$

Heather Z.
Heather Z.
Numerade Educator
00:38

Problem 71

Find all intercepts for each line. Some of these lines have only one intercept.
$$y=5 x$$

Heather Z.
Heather Z.
Numerade Educator
00:43

Problem 72

Find all intercepts for each line. Some of these lines have only one intercept.
$$y=-4 x$$

Heather Z.
Heather Z.
Numerade Educator
00:41

Problem 73

Find all intercepts for each line. Some of these lines have only one intercept.
$$6 x+3=0$$

Heather Z.
Heather Z.
Numerade Educator
00:40

Problem 74

Find all intercepts for each line. Some of these lines have only one intercept.
$$40 x+5=0$$

Heather Z.
Heather Z.
Numerade Educator
00:52

Problem 75

Find all intercepts for each line. Some of these lines have only one intercept.
$$12+18 y=0$$

Heather Z.
Heather Z.
Numerade Educator
00:42

Problem 76

Find all intercepts for each line. Some of these lines have only one intercept.
$$2-10 y=0$$

Heather Z.
Heather Z.
Numerade Educator
01:02

Problem 77

Find all intercepts for each line. Some of these lines have only one intercept.
$$2-4 y=8 x$$

Heather Z.
Heather Z.
Numerade Educator
01:02

Problem 78

Find all intercepts for each line. Some of these lines have only one intercept.
$$9 x+3=12 y$$

Heather Z.
Heather Z.
Numerade Educator
00:43

Problem 79

Complete the given ordered pairs so that each ordered pair satisfies the given equation.
$$(2, \quad),(\quad,-3), \quad y=-3 x+6$$

Heather Z.
Heather Z.
Numerade Educator
00:49

Problem 80

Complete the given ordered pairs so that each ordered pair satisfies the given equation.
$$(-1,\quad),(\quad, 4), \quad y=\frac{1}{2} x+2$$

Heather Z.
Heather Z.
Numerade Educator
01:09

Problem 81

Complete the given ordered pairs so that each ordered pair satisfies the given equation.
$$
(-4,\quad),(\quad, 6),\quad \frac{1}{2} x-\frac{1}{3} y=9
$$

Heather Z.
Heather Z.
Numerade Educator
01:02

Problem 82

Complete the given ordered pairs so that each ordered pair satisfies the given equation.
$$(3, \quad),(\quad,-1), \quad 2 x-3 y=5$$

Heather Z.
Heather Z.
Numerade Educator
02:07

Problem 83

Solve each problem.
The rising base price $P$ (in dollars) for a new Ford $\mathrm{F} 150$ can be modeled by the function $P=793 n+15,950,$ where $n$ is the number of years since 2000.
a) What will be the base price for a new Ford F150 in $2009 ?$
b) By what amount is the price increasing annually?
c) Graph the equation for $0 \leq n \leq 10$

Heather Z.
Heather Z.
Numerade Educator
02:13

Problem 84

Solve each problem.
The 2006 average retail price $P$ (in dollars) for an $n$ -year-old Toyota Camry can be modeled by the function $P=22,667-1832 n$ where $0 \leq n \leq 4$.
a) What was the average retail price of a 4 -year-old Camry in $2006 ?$
b) By what amount does this model depreciate annually?
c) Graph the equation for $0 \leq n \leq 4$.

Heather Z.
Heather Z.
Numerade Educator
01:25

Problem 85

Solve each problem.
For a one-day car rental the X-press Car Company charges $C$ dollars, where $C$ is determined by the function $C=0.26 m+42$ and $m$ is the number of miles driven.
a) What is the charge for a car driven 400 miles?
b) Sketch a graph of the equation for $m$ ranging from 0 to 1000

Heather Z.
Heather Z.
Numerade Educator
01:30

Problem 86

Solve each problem.
The Friendly Bob Loan Company gives each applicant a rating, $t,$ from 0 to 10 according to the applicant's ability to repay, a higher rating indicating higher risk. The interest rate, $r$, is then determined by the function $r=0.02 t+0.15$
a) If your rating were $8,$ then what would be your interest rate?
b) Sketch the graph of the equation for $t$ ranging from 0 to 10

Heather Z.
Heather Z.
Numerade Educator
01:18

Problem 87

Solve each problem.
The function $C=0.50 t+8.95$ gives the customer's cost in dollars for a pan pizza, where $t$ is the number of toppings.
a) Find the cost of a five-topping pizza.
b) Find $t$ if $C=14.45$ and interpret your result.

Heather Z.
Heather Z.
Numerade Educator
01:58

Problem 88

Solve each problem.
The function $L=0.10 n+4.95$ gives the monthly bill in dollars for AT\&T's one-rate plan, where $n$ is the number of minutes of long distance used during the month.
a) Find $n$ if the long distance charge is $\$ 23.45$
b) Find $L$ for 120 minutes.
c) Estimate the $L$ -intercept from the accompanying graph.
d) Use the formula to find the $L$ -intercept.
e) Use the formula to find the $n$ -intercept.
(GRAPH CAN'T COPY)

Heather Z.
Heather Z.
Numerade Educator
02:26

Problem 89

Solve each problem.
An office manager is placing an order for note pads at $\$ 1$ each and binders at $\$ 2$ each. The total cost of the order must be $\$ 100 .$ Write an equation for the total cost and graph it. If he orders 30 note pads, then how many binders must he order?

Heather Z.
Heather Z.
Numerade Educator
02:36

Problem 90

Solve each problem.
Jessenda is ordering tacos at $\$ 0.75$ each and burritos at $\$ 2$ each for a large group. She must spend $\$ 300 .$ Write an equation for the total cost and graph it. If she orders 200 tacos, then how many burritos must she order?

Heather Z.
Heather Z.
Numerade Educator
03:50

Problem 91

Solve each problem.
Hillary sells roses at a busy Los Angeles intersection. The functions$$\begin{array}{l}C=0.55 x+50 \\R=1.50 x\end{array}$$and$$P=0.95 x-50$$ give her weekly cost, revenue, and profit in terms of $x$ where $x$ is the number of roses that she sells in one week.
a) Find $C, R,$ and $P$ if $x=850 .$ Interpret your results.
b) Find $x$ if $P=995$ and interpret your result.
c) Find $R-C$ if $x=1100$ and interpret your result.

Heather Z.
Heather Z.
Numerade Educator
02:37

Problem 92

Solve each problem.
A pop up off the bat of Mark McGwire goes straight into the air at 88 feet per second $(\mathrm{ft} / \mathrm{sec}) .$ The function $v=-32 t+88$ gives the velocity of the ball in feet per second, $t$ seconds after the ball is hit.
a) Find the velocity for $t=2$ and $t=3$ seconds. What does a negative velocity mean?
b) For what value of $t$ is $v=0 ?$ Where is the ball at this time?
c) What are the two intercepts on the accompanying graph? Interpret this answer.
d) If the ball takes the same time going up as it does coming down, then what is its velocity as it hits the ground?
(GRAPH CAN'T COPY)

Heather Z.
Heather Z.
Numerade Educator

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