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Beginning Algebra

Margaret L. Lial, John Hornsby

Chapter 3

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

Educators

AG

Section 1

Linear Equations in Two Variables; The Rectangular Coordinate System

01:25

Problem 1

The line graph shows the overall unemployment rate in the U.S. civilian labor force in August of the years 2003 through 2009.
Between which pairs of consecutive years did the unemployment rate decrease?

AG
Angel Garcia Mejia
Numerade Educator
00:30

Problem 2

The line graph shows the overall unemployment rate in the U.S. civilian labor force in August of the years 2003 through 2009.
What was the general trend in the unemployment rate between 2007 and $2009 ?$

AG
Angel Garcia Mejia
Numerade Educator
01:10

Problem 3

The line graph shows the overall unemployment rate in the U.S. civilian labor force in August of the years 2003 through 2009.
Estimate the overall unemployment rate in 2003 and $2004 .$ About how much did the unemployment rate decline between 2003 and $2004 ?$

AG
Angel Garcia Mejia
Numerade Educator
00:44

Problem 4

The line graph shows the overall unemployment rate in the U.S. civilian labor force in August of the years 2003 through 2009.
During which year(s)
(a) was the unemployment rate greater than $6 \%,$ but less than $7 \% ?$
(b) did the unemployment rate stay the same?

AG
Angel Garcia Mejia
Numerade Educator
01:30

Problem 5

The symbol $(x, y) \frac{ }{(\text { does/does not })}$ represent an ordered pair, while the symbols $[x, y]$ and $\{x, y\} \frac{ \text { } }{(\text { do/do not })}$ represent ordered pairs.

AG
Angel Garcia Mejia
Numerade Educator
00:57

Problem 6

The ordered pair $(3,2)$ is a solution of the equation $2 x-5 y=$

AG
Angel Garcia Mejia
Numerade Educator
01:08

Problem 7

The point whose graph has coordinates $(-4,2)$ is in quadrant

AG
Angel Garcia Mejia
Numerade Educator
00:55

Problem 8

The point whose graph has coordinates $(0,5)$ lies on the _______-axis

AG
Angel Garcia Mejia
Numerade Educator
00:35

Problem 9

The ordered pair $(4,___)$ is a solution of the equation $y=3$

AG
Angel Garcia Mejia
Numerade Educator
00:27

Problem 10

The ordered pair $(__,-2)$ is a solution of the equation $x=6$

AG
Angel Garcia Mejia
Numerade Educator
00:36

Problem 11

Decide whether the given ordered pair is a solution of the given equation.
$$
x+y=8 ; \quad(0,8)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:37

Problem 12

Decide whether the given ordered pair is a solution of the given equation.
$$
x+y=9 ; \quad(0,9)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:57

Problem 13

Decide whether the given ordered pair is a solution of the given equation.
$$
2 x+y=5 ; \quad(3,-1)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:50

Problem 14

Decide whether the given ordered pair is a solution of the given equation.
$$
2 x-y=6 ; \quad(4,2)
$$

AG
Angel Garcia Mejia
Numerade Educator
01:00

Problem 15

Decide whether the given ordered pair is a solution of the given equation.
$$
5 x-3 y=15 ; \quad(5,2)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:52

Problem 16

Decide whether the given ordered pair is a solution of the given equation.
$$
4 x-3 y=6 ; \quad(2,1)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:42

Problem 17

Decide whether the given ordered pair is a solution of the given equation.
$$
x=-4 y ; \quad(-8,2)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:38

Problem 18

Decide whether the given ordered pair is a solution of the given equation.
$$
y=3 x ; \quad(2,6)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:28

Problem 19

Decide whether the given ordered pair is a solution of the given equation.
$$
y=2 ; \quad(4,2)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:35

Problem 20

Decide whether the given ordered pair is a solution of the given equation.
$$
x=-6 ;(-6,5)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:35

Problem 21

Decide whether the given ordered pair is a solution of the given equation.
$$
x-6=0 ; \quad(4,2)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:38

Problem 22

Decide whether the given ordered pair is a solution of the given equation.
$$
x+4=0 ; \quad(-6,2)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:55

Problem 23

Complete each ordered pair for the equation $y=2 x+7$
$$
(5,___)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:41

Problem 24

Complete each ordered pair for the equation $y=2 x+7$
$$
(2,___)
$$

AG
Angel Garcia Mejia
Numerade Educator
01:11

Problem 25

Complete each ordered pair for the equation $y=2 x+7$
$$
(__,-3)
$$

AG
Angel Garcia Mejia
Numerade Educator
12:29

Problem 26

Complete each ordered pair for the equation $y=2 x+7$
$$
(__, 0)
$$

Maria Giefer
Maria Giefer
Numerade Educator
01:00

Problem 27

Complete each ordered pair for the equation $y=-4 x-4$
$$
(__, 0)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:30

Problem 28

Complete each ordered pair for the equation $y=-4 x-4$
$$
(0,__)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:50

Problem 29

Complete each ordered pair for the equation $y=-4 x-4$
$$
(__, 24)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:37

Problem 30

Complete each ordered pair for the equation $y=-4 x-4$
$$
(__, 16)
$$

AG
Angel Garcia Mejia
Numerade Educator
01:52

Problem 31

Complete each table of values. Write the results as ordered pairs.
$$
4 x+3 y=24
$$

AG
Angel Garcia Mejia
Numerade Educator
01:17

Problem 32

Complete each table of values. Write the results as ordered pairs.
$$
2 x+3 y=12
$$

AG
Angel Garcia Mejia
Numerade Educator
01:18

Problem 33

Complete each table of values. Write the results as ordered pairs.
$$
4 x-9 y=-36
$$

AG
Angel Garcia Mejia
Numerade Educator
01:21

Problem 34

Complete each table of values. Write the results as ordered pairs.
$$
3 x-5 y=-15
$$

AG
Angel Garcia Mejia
Numerade Educator
00:33

Problem 35

Complete each table of values. Write the results as ordered pairs.
$$
x=12
$$

AG
Angel Garcia Mejia
Numerade Educator
00:26

Problem 36

Complete each table of values. Write the results as ordered pairs.
$$
x=-9
$$

AG
Angel Garcia Mejia
Numerade Educator
00:31

Problem 37

Complete each table of values. Write the results as ordered pairs.
$$
y=-10
$$

AG
Angel Garcia Mejia
Numerade Educator
00:29

Problem 38

Complete each table of values. Write the results as ordered pairs.
$$
y=-6
$$

AG
Angel Garcia Mejia
Numerade Educator
00:29

Problem 39

Complete each table of values. Write the results as ordered pairs.
$$
y+2=0
$$

AG
Angel Garcia Mejia
Numerade Educator
00:30

Problem 40

Complete each table of values. Write the results as ordered pairs.
$$
y+6=0
$$

AG
Angel Garcia Mejia
Numerade Educator
00:28

Problem 41

Complete each table of values. Write the results as ordered pairs.
$$
x-4=0
$$

AG
Angel Garcia Mejia
Numerade Educator
00:31

Problem 42

Complete each table of values. Write the results as ordered pairs.
$$
x-8=0
$$

AG
Angel Garcia Mejia
Numerade Educator
01:42

Problem 43

Do $(3,4)$ and $(4,3)$ correspond to the same point in the plane? Explain.

Nichola Wallace
Nichola Wallace
Numerade Educator

Problem 44

$\mathrm{Do}(4,-1)$ and $(-1,4)$ represent the same ordered pair? Explain.

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02:16

Problem 45

Give the ordered pairs for the points labeled $A-F$ in the figure. (All coordinates are integers.) Tell the quadrant in which each point is located. See Example $5 .$

AG
Angel Garcia Mejia
Numerade Educator
00:44

Problem 46

Give the ordered pairs for the points labeled $A-F$ in the figure. (All coordinates are integers.) Tell the quadrant in which each point is located. See Example $5 .$
The origin is represented by the ordered pair

AG
Angel Garcia Mejia
Numerade Educator
00:32

Problem 47

Plot and label each point in a rectangular coordinate system.
$$
(6,2)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:26

Problem 48

Plot and label each point in a rectangular coordinate system.
$$
(5,3)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:35

Problem 49

Plot and label each point in a rectangular coordinate system.
$$
(-4,2)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:31

Problem 50

Plot and label each point in a rectangular coordinate system.
$$
(-3,5)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:57

Problem 51

Plot and label each point in a rectangular coordinate system.
$$
\left(-\frac{4}{5},-1\right)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:46

Problem 52

Plot and label each point in a rectangular coordinate system.
$$
\left(-\frac{3}{2},-4\right)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:33

Problem 53

Plot and label each point in a rectangular coordinate system.
$$
(3,-1.75)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:37

Problem 54

Plot and label each point in a rectangular coordinate system.
$$
(5,-4.25)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:24

Problem 55

Plot and label each point in a rectangular coordinate system.
$$
(0,4)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:17

Problem 56

Plot and label each point in a rectangular coordinate system.
$$
(0,-3)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:21

Problem 57

Plot and label each point in a rectangular coordinate system.
$$
(4,0)
$$

AG
Angel Garcia Mejia
Numerade Educator
00:21

Problem 58

Plot and label each point in a rectangular coordinate system.
$$
(-3,0)
$$

AG
Angel Garcia Mejia
Numerade Educator

Problem 59

Fill in each blank with the word positive or the word negative. The point with coordinates is in
quadrant III if $x$ is _____ and $y$ is ______

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Problem 60

Fill in each blank with the word positive or the word negative. The point with coordinates is in quadrant II if $x$ is _____ and $y$ is________

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Problem 61

Fill in each blank with the word positive or the word negative. The point with coordinates is in
quadrant IV if $x$ is ______ and $y$ is _______

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Problem 62

Fill in each blank with the word positive or the word negative. The point with coordinates is in
quadrant I if $x$ is _____ and $y$ is ______

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Problem 63

A point $(x, y)$ has the property that $x y<0 .$ In which quadrant(s) must the point lie? Explain.

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Problem 64

A point $(x, y)$ has the property that $x y>0 .$ In which quadrant(s) must the point lie? Explain.

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02:44

Problem 65

Complete each table of values. Then plot and label the ordered pairs.
$$
x-2 y=6
$$

AG
Angel Garcia Mejia
Numerade Educator
01:44

Problem 66

Complete each table of values. Then plot and label the ordered pairs.
$$
2 x-y=4
$$

AG
Angel Garcia Mejia
Numerade Educator
02:13

Problem 67

Complete each table of values. Then plot and label the ordered pairs.
$$
3 x-4 y=12
$$

AG
Angel Garcia Mejia
Numerade Educator
01:58

Problem 68

Complete each table of values. Then plot and label the ordered pairs.
$$
2 x-5 y=10
$$

AG
Angel Garcia Mejia
Numerade Educator
00:58

Problem 69

Complete each table of values. Then plot and label the ordered pairs.
$$
y+4=0
$$

AG
Angel Garcia Mejia
Numerade Educator
00:52

Problem 70

Complete each table of values. Then plot and label the ordered pairs.
$$
x-5=0
$$

AG
Angel Garcia Mejia
Numerade Educator
00:47

Problem 71

Look at your graphs of the ordered pairs in Exercises 65–70. Describe the pattern indicated by the plotted points.

AG
Angel Garcia Mejia
Numerade Educator

Problem 72

(a) A line through the plotted points in Exercise 69 would be horizontal. What do you notice about the y-coordinates of the ordered pairs?
(b) A line through the plotted points in Exercise 70 would be vertical. What do you notice about the x-coordinates of the ordered pairs?

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00:38

Problem 73

Solve each problem.
It costs a flat fee of $\$ 20$ plus $\$ 5$ per day to rent a pressure washer. Therefore, the cost to rent the pressure washer for $x$ days is given by
$$
y=5 x+20
$$
where $y$ is in dollars. Express each of the following as an ordered pair.
(a) When the washer is rented for 5 days, the cost is $\$ 45 .$
(b) I paid $\$ 50$ when I returned the washer, so I must have rented it for 6 days.

AG
Angel Garcia Mejia
Numerade Educator
01:39

Problem 74

Solve each problem.
Suppose that it costs $\$ 5000$ to start up a business selling snow cones. Furthermore, it costs $\$ 0.50$ per cone in labor, ice, syrup, and overhead. Then the cost to make $x$ snow cones is given by $y$ dollars, where
$$
y=0.50 x+5000
$$
Express each of the following as an ordered pair.
(a) When 100 snow cones are made, the cost is $\$ 5050$.
(b) When the cost is $\$ 6000$, the number of snow cones made is 2000 .

AG
Angel Garcia Mejia
Numerade Educator
03:03

Problem 75

The table shows the rate (in percent) at which 2-year college students (public) completed a degree within 3 years.
(a) Write the data from the table as ordered pairs $(x, y),$ where $x$ represents the year and $y$ represents the percent.
(b) What does the ordered pair $(2007,26.9)$ mean in the context of this problem?
(c) Make a scatter diagram of the data, using the ordered pairs from part (a) and the given grid.
(d) Describe the pattern indicated by the points on the scatter diagram. What is happening to rates at which 2 -year college students complete a degree within 3 years?

AG
Angel Garcia Mejia
Numerade Educator
02:11

Problem 76

The table shows the number of U.S. students who studied abroad (in thousands) for several academic years.
(a) Write the data from the table as ordered pairs $(x, y),$ where $x$ represents the year and
$y$ represents the number of U.S. students (in thousands) studying abroad.
(b) What does the ordered pair $(2006,242)$ mean in the context of this problem?
(c) Make a scatter diagram of the data, using the ordered pairs from part (a) and the given grid.
(d) Describe the pattern indicated by the points on the scatter diagram. What was the trend in the number of U.S. students studying abroad during these years?

AG
Angel Garcia Mejia
Numerade Educator
03:31

Problem 77

The maximum benefit for the heart from exercising occurs if the heart rate is in the target heart rate zone. The lower limit of this target zone can be approximated by the linear equation
$$
y=-0.65 x+143
$$
where $x$ represents age and $y$ represents heartbeats per minute. (Source: The Gazette.)
(a) Complete the table of values for this linear equation.
(b) Write the data from the table of values as ordered pairs.
(c) Make a scatter diagram of the data. Do the points lie in an approximately linear pattern?

AG
Angel Garcia Mejia
Numerade Educator
03:30

Problem 78

(See Exercise $77 .$ ) The upper limit of the target heart rate zone can be approximated by the linear equation
$$
y=-0.85 x+187
$$
where $x$ represents age and $y$ represents heartbeats per minute.
(a) Complete the table of values for this linear equation.
(b) Write the data from the table of values as ordered pairs.
(c) Make a scatter diagram of the data. Describe the pattern indicated by the data.

AG
Angel Garcia Mejia
Numerade Educator
00:48

Problem 79

See Exercises 77 and $78 .$ What is the target heart rate zone for age $20 ?$ Age $40 ?$

AG
Angel Garcia Mejia
Numerade Educator
00:38

Problem 80

See Exercises 77 and $78 .$ What is the target heart rate zone for age $60 ?$ Age $80 ?$

AG
Angel Garcia Mejia
Numerade Educator
00:19

Problem 81

Solve each equation.
$$
3 x+6=0
$$

AG
Angel Garcia Mejia
Numerade Educator
00:16

Problem 82

Solve each equation.
$$
4+2 x=10
$$

AG
Angel Garcia Mejia
Numerade Educator
00:19

Problem 83

Solve each equation.
$$
9-x=-4
$$

AG
Angel Garcia Mejia
Numerade Educator
00:17

Problem 84

Solve each equation.
$$
-5+t=3
$$

AG
Angel Garcia Mejia
Numerade Educator