Contents

Chapter 4

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4.1

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 2, 1) is plotted and labeled "a". The point (negative 3, negative 1) is plotted and labeled "b". The point (4, negative 4) is plotted and labeled "c". The point (negative 4, negative one half) is plotted and labeled “d”.

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4.2

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 4, 1) is plotted and labeled "a". The point (negative 2, 3) is plotted and labeled "b". The point (2, negative 5) is plotted and labeled "c". The point (negative 3, 2 and one half) is plotted and labeled “d”.

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4.3

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled.

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4.4

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (negative 5, 0), (3, 0), (0, 0), (0, negative 1), and (0, 4) are plotted and labeled.

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4.5

A: $(5, 1) (5, 1)$ B: $(−2, 4) (−2, 4)$ C: $(−5, −1) (−5, −1)$ D: $(3, −2) (3, −2)$ E: $(0, −5) (0, −5)$ F: $(4, 0) (4, 0)$

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4.6

A: $(4, 2) (4, 2)$ B: $(−2, 3) (−2, 3)$ C: $(−4, −4) (−4, −4)$ D: $(3, −5) (3, −5)$ E: $(−3, 0) (−3, 0)$ F: $(0, 2) (0, 2)$

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4.7

a, c

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4.8

b, c

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4.9

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4.10

a, b

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4.11

$y = 3 x - 1 y = 3 x - 1$
$x x$	$y y$	$(x, y) (x, y)$
0	$−1 −1$	$(0, −1) (0, −1)$
$−1 −1$	$−4 −4$	$(−1, −4) (−1, −4)$
2	5	$(2, 5) (2, 5)$

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4.12

$y = 6 x + 1 y = 6 x + 1$
$x x$	$y y$	$(x, y) (x, y)$
0	1	$(0, 1) (0, 1)$
1	7	$(1, 7) (1, 7)$
$−2 −2$	$−11 −11$	$(−2, −11) (−2, −11)$

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4.13

$2 x - 5 y = 20 2 x - 5 y = 20$
$x x$	$y y$	$(x, y) (x, y)$
0	$−4 −4$	$(0, −4) (0, −4)$
10	0	$(10, 0) (10, 0)$
$−5 −5$	$−6 −6$	$(−5, −6) (−5, −6)$

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4.14

$3 x - 4 y = 12 3 x - 4 y = 12$
$x x$	$y y$	$(x, y) (x, y)$
0	$−3 −3$	$(0, −3) (0, −3)$
4	0	$(4, 0) (4, 0)$
$−4 −4$	$−6 −6$	$(−4, −6) (−4, −6)$

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4.15

Answers will vary.

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4.16

Answers will vary.

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4.17

Answers will vary.

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4.18

Answers will vary.

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4.19

ⓐ yes, yes ⓑ yes, yes

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4.20

ⓐ no, no ⓑ yes, yes

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4.21

The figure shows a straight line on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 2, negative 7), (negative 1, negative 5), (0, negative 3), (1, negative 1), (2, 1), (3, 3), (4, 5), and (5, 7). There are arrows at the ends of the line pointing to the outside of the figure.

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4.22

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4.23

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 2, 8), (0, 0), and (2, negative 8). The line has arrows on both ends pointing to the outside of the figure.

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4.24

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4.25

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4.26

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4.27

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4.28

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4.29

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The straight line goes through the points (negative 1, 6), (0, 4), (1, 2), (2, 0), (3, negative 2), and (4, negative 4). The line has arrows on both ends pointing to the outside of the figure.

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4.30

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4.31

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (5, 1), (5, 2), (5, 3), and all other points with first coordinate 5. The line has arrows on both ends pointing to the outside of the figure.

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4.32

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4.33

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. The straight line goes through the points (negative 4, negative 4), (0, negative 4), (4, negative 4), and all other points with second coordinate negative 4. The line has arrows on both ends pointing to the outside of the figure.

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4.34

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4.35

The figure shows a two straight lines drawn on the same x y-coordinate plane. The x-axis of the plane runs from negative 12 to 12. The y-axis of the plane runs from negative 12 to 12. One line is a straight horizontal line going through the points (negative 4, negative 4), (0, negative 4), (4, negative 4), and all other points with second coordinate negative 4. The other line is a slanted line going through the points (negative 2, 8), (negative 1, 4), (0, 0), (1, negative 4), and (2, negative 8).

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4.36

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4.37

x- intercept: $(2, 0) (2, 0)$ ; y- intercept: $(0, −2) (0, −2)$

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4.38

x- intercept: $(3, 0) (3, 0)$ , y- intercept: $(0, 2) (0, 2)$

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4.39

x- intercept: $(4, 0) (4, 0)$ , y- intercept: $(0, 12) (0, 12)$

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4.40

x- intercept: $(8, 0) (8, 0)$ , y- intercept: $(0, 2) (0, 2)$

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4.41

x- intercept: $(4, 0) (4, 0)$ , y- intercept: $(0, −3) (0, −3)$

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4.42

x- intercept: $(4, 0) (4, 0)$ , y- intercept: $(0, −2) (0, −2)$

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4.43

The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 12 to 12. The y- axis of the planes runs from negative 12 to 12. The straight line goes through the points (negative 10, negative 7), (negative 8, negative 6), (negative 6, negative 5), (negative 4, negative 4), (negative 2, negative 3), (0, negative 2), (2, negative 1), (4, 0), (6, 1), (8, 2), and (10, 3).

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4.44

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4.45

The figure shows the graph of a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 7 to 7. The y- axis of the planes runs from negative 7 to 7. The straight line goes through the points (0, negative 5), (2, 0), and (4, 5).

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4.46

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4.47

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4.48

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4.49

$\frac{4}{3} \frac{4}{3}$

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4.50

$\frac{1}{4} \frac{1}{4}$

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4.51

$- \frac{2}{3} - \frac{2}{3}$

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4.52

$- \frac{4}{3} - \frac{4}{3}$

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4.53

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 2, row 3, the peg in column 2, row 4 and the peg in column 5, row 3, forming a right triangle. The 2, 3 peg forms the vertex of the 90 degree angle and the line from the 2, 4 peg to the 5, 3 peg forms the hypotenuse of the triangle.

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4.54

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 1, the peg in column 1, row 4 and the peg in column 3, row 1, forming a right triangle. The 1, 1 peg forms the vertex of the 90 degree angle and the line from the 1, 4 peg to the 3, 1 peg forms the hypotenuse of the triangle.

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4.55

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4.56

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4.57

$\frac{2}{5} \frac{2}{5}$

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4.58

$\frac{3}{4} \frac{3}{4}$

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4.59

$- \frac{4}{3} - \frac{4}{3}$

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4.60

$- \frac{3}{5} - \frac{3}{5}$

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4.61

$\frac{5}{4} \frac{5}{4}$

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4.62

$\frac{3}{2} \frac{3}{2}$

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4.63

undefined

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4.64

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4.65

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4.66

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4.67

$−1 −1$

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4.68

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4.69

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 4, negative 10) and (2, negative 2).

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4.70

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 2, 3) and (10, 6).

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4.71

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line intercepts the y-axis at (0, 4) and passes through the point (4, negative 6).

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4.72

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line intercepts the x-axis at (negative 3, 0) and passes through the point (1, negative 3).

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4.73

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (negative 2, 1) and (negative 1, 4).

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4.74

The graph shows the x y coordinate plane. The x and y-axes run from negative 7 to 7. A line passes through the points (4, negative 2) and (5, negative 4).

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4.75

$\frac{7}{12} \frac{7}{12}$

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4.76

$\frac{5}{12} \frac{5}{12}$

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4.77

$- \frac{1}{36} - \frac{1}{36}$

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4.78

$- \frac{1}{48} - \frac{1}{48}$

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4.79

slope $m = \frac{2}{3} m = \frac{2}{3}$ and y-intercept $(0, −1) (0, −1)$

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4.80

slope $m = \frac{1}{2} m = \frac{1}{2}$ and y-intercept $(0, 3) (0, 3)$

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4.81

$\frac{2}{5}; (0, −1) \frac{2}{5}; (0, −1)$

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4.82

$- \frac{4}{3}; (0, 1) - \frac{4}{3}; (0, 1)$

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4.83

$- \frac{1}{4}; (0, 2) - \frac{1}{4}; (0, 2)$

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4.84

$- \frac{3}{2}; (0, 6) - \frac{3}{2}; (0, 6)$

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4.85

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The points (0, 1) and (1, 5) are plotted on the line.

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4.86

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4.87

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4.88

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4.89

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4.90

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4.91

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4.92

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4.93

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 70 to 30. The y-axis of the plane runs from negative 20 to 40. The points (0, 25) and (10, 30) are plotted on the line.

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4.94

The figure shows a line graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 50 to 350. The y-axis of the plane runs from negative 40 to 40. The points (0, negative 30) and (100, negative 20) are plotted on the line.

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4.95

ⓐ intercepts ⓑ horizontal line ⓒ slope–intercept ⓓ vertical line

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4.96

ⓐ vertical line ⓑ slope–intercept ⓒ horizontal line ⓓ intercepts

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4.97

ⓐ 50 inches
ⓑ 66 inches
ⓒ The slope, 2, means that the height, h, increases by 2 inches when the shoe size, s, increases by 1. The h-intercept means that when the shoe size is 0, the height is 50 inches.
ⓓ

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4.98

ⓐ 40 degrees
ⓑ 65 degrees
ⓒ The slope, $\frac{1}{4} \frac{1}{4}$ , means that the temperature Fahrenheit (F) increases 1 degree when the number of chirps, n, increases by 4. The T-intercept means that when the number of chirps is 0, the temperature is $40 ° 40 °$ .
ⓓ

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4.99

ⓐ $60
ⓑ $185
ⓒ The slope, 0.5, means that the weekly cost, C, increases by $0.50 when the number of miles driven, n, increases by 1. The C-intercept means that when the number of miles driven is 0, the weekly cost is $60
ⓓ

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4.100

ⓐ $35
ⓑ $170
ⓒ The slope, 1.8, means that the weekly cost, C, increases by $1.80 when the number of invitations, n, increases by 1.80.
The C-intercept means that when the number of invitations is 0, the weekly cost is $35.;
ⓓ

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4.101

parallel

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4.102

parallel

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4.103

parallel

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4.104

parallel

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4.105

parallel

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4.106

parallel

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4.107

not parallel; same line

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4.108

not parallel; same line

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4.109

perpendicular

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4.110

perpendicular

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4.111

not perpendicular

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4.112

not perpendicular

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4.113

$y = \frac{2}{5} x + 4 y = \frac{2}{5} x + 4$

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4.114

$y = − x - 3 y = − x - 3$

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4.115

$y = \frac{3}{5} x + 1 y = \frac{3}{5} x + 1$

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4.116

$y = \frac{4}{3} x - 5 y = \frac{4}{3} x - 5$

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4.117

$y = \frac{5}{6} x - 2 y = \frac{5}{6} x - 2$

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4.118

$y = \frac{2}{3} x - 4 y = \frac{2}{3} x - 4$

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4.119

$y = - \frac{2}{5} x - 1 y = - \frac{2}{5} x - 1$

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4.120

$y = - \frac{3}{4} x - 4 y = - \frac{3}{4} x - 4$

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4.121

$y = 8 y = 8$

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4.122

$y = 4 y = 4$

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4.123

$y = \frac{5}{2} x - \frac{13}{2} y = \frac{5}{2} x - \frac{13}{2}$

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4.124

$y = - \frac{2}{5} x + \frac{22}{5} y = - \frac{2}{5} x + \frac{22}{5}$

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4.125

$y = \frac{1}{3} x - \frac{10}{3} y = \frac{1}{3} x - \frac{10}{3}$

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4.126

$y = - \frac{2}{5} x - \frac{23}{5} y = - \frac{2}{5} x - \frac{23}{5}$

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4.127

$x = 5 x = 5$

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4.128

$x = −4 x = −4$

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4.129

$y = 3 x - 10 y = 3 x - 10$

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4.130

$y = \frac{1}{2} x + 1 y = \frac{1}{2} x + 1$

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4.131

$y = - \frac{1}{3} x + \frac{10}{3} y = - \frac{1}{3} x + \frac{10}{3}$

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4.132

$y = −2 x + 16 y = −2 x + 16$

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4.133

$y = −5 y = −5$

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4.134

$y = −1 y = −1$

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4.135

$x = −5 x = −5$

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4.136

$x = −4 x = −4$

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4.137

ⓐ yes ⓑ yes ⓒ yes ⓓ yes ⓔ no

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4.138

ⓐ yes ⓑ yes ⓒ no ⓓ no ⓔ yes

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4.139

$y \geq −2 x + 3 y \geq −2 x + 3$

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4.140

$y < \frac{1}{2} x - 4 y < \frac{1}{2} x - 4$

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4.141

$x - 4 y \leq 8 x - 4 y \leq 8$

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4.142

$3 x - y \leq 6 3 x - y \leq 6$

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4.143

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals five-halves x minus 4 is plotted as a solid arrow extending from the bottom left toward the top right. The region above the line is shaded.

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4.144

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals two-thirds x minus 5 is plotted as a dashed arrow extending from the bottom left toward the top right. The region below the line is shaded.

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4.145

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line 2 x minus 3 y equals 6 is plotted as a solid arrow extending from the bottom left toward the top right. The region above the line is shaded.

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4.146

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line 2 x minus y equals 3 is plotted as a dashed arrow extending from the bottom left toward the top right. The region below the line is shaded.

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4.147

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 3 x is plotted as a dashed arrow extending from the top left toward the bottom right. The region to the right of the line is shaded.

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4.148

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 2 x is plotted as a solid arrow extending from the top left toward the bottom right. The region to the right of the line is shaded.

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4.149

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals 5 is plotted as a dashed arrow horizontally across the plane. The region above the line is shaded.

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4.150

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 1 is plotted as a dashed arrow horizontally across the plane. The region below the line is shaded.

Section 4.1 Exercises

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The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 4, 2) is plotted and labeled "a". The point (negative 1, negative 2) is plotted and labeled "b". The point (3, negative 5) is plotted and labeled "c". The point (negative 3, 5) is plotted and labeled “d”. The point (5 thirds, 2) is plotted and labeled “e”.

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The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (3, negative 1) is plotted and labeled "a". The point (negative 3, 1) is plotted and labeled "b". The point (negative 2, 2) is plotted and labeled "c". The point (negative 4, negative 3) is plotted and labeled “d”. The point (1, 14 fifths) is plotted and labeled “e”.

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The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 2, 0) is plotted and labeled "a". The point (negative 3, 0) is plotted and labeled "b". The point (0, 0) is plotted and labeled "c". The point (0, 4) is plotted and labeled “d”. The point (0, 3) is plotted and labeled “e”.

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The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (0, 0) is plotted and labeled "a". The point (0, negative 3) is plotted and labeled "b". The point (negative 4, 0) is plotted and labeled "c". The point (1, 0) is plotted and labeled “d”. The point (0, negative 2) is plotted and labeled “e”.

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A: $(−4, 1) (−4, 1)$ B: $(−3, −4) (−3, −4)$ C: $(1, −3) (1, −3)$ D: $(4, 3) (4, 3)$

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11.

A: $(0, −2) (0, −2)$ B: $(−2, 0) (−2, 0)$ C: $(0, 5) (0, 5)$ D: $(5, 0) (5, 0)$

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13.

a, b

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15.

a, c

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17.

b, c

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19.

a, b

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21.

$x x$	$y y$	$(x, y) (x, y)$
0	$−4 −4$	$(0, −4) (0, −4)$
2	0	$(2, 0) (2, 0)$
$−1 −1$	$−6 −6$	$(−1, −6) (−1, −6)$

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23.

$x x$	$y y$	$(x, y) (x, y)$
0	5	$(0, 5) (0, 5)$
3	2	$(3, 2) (3, 2)$
$−2 −2$	7	$(−2, 7) (−2, 7)$

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25.

$x x$	$y y$	$(x, y) (x, y)$
0	1	$(0, 1) (0, 1)$
3	2	$(3, 2) (3, 2)$
6	3	$(6, 3) (6, 3)$

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27.

$x x$	$y y$	$(x, y) (x, y)$
0	$−2 −2$	$(0, −2) (0, −2)$
2	$−5 −5$	$(2, −5) (2, −5)$
$−2 −2$	1	$(−2, 1) (−2, 1)$

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29.

$x x$	$y y$	$(x, y) (x, y)$
0	2	$(0, 2) (0, 2)$
3	4	$(3, 1) (3, 1)$
6	0	$(6, 0) (6, 0)$

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31.

$x x$	$y y$	$(x, y) (x, y)$
0	$−2 −2$	$(0, −2) (0, −2)$
10	2	$(10, 2) (10, 2)$
5	0	$(5, 0) (5, 0)$

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33.

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35.

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37.

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39.

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41.

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43.

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45.

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47.

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49.

ⓐ

The graph shows the x y-coordinate plane. The x- and y-axes each run from 0 to 25. The points (0, 7), (2, 11), (4, 15), (6, 16), (8, 19), (10, 20) and (12, 21) are plotted and labeled.

ⓑ Age and weight are only positive.

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51.

Answers will vary.

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53.

Answers will vary.

Section 4.2 Exercises

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55.

ⓐ yes; no ⓑ no; no ⓒ yes; yes ⓓ yes; yes

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57.

ⓐ yes; yes ⓑ yes; yes ⓒ yes; yes ⓓ no; no

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59.

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61.

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63.

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65.

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67.

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69.

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71.

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73.

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75.

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77.

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79.

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81.

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83.

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85.

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87.

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to -7. The equation 3 x plus y equals 7 is graphed.

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89.

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91.

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93.

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95.

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97.

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99.

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101.

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103.

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105.

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107.

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109.

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111.

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113.

The figure shows a straight horizontal line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The horizontal line goes through the points (0, negative 15/4), (1, negative 15/4), (2, negative 15/4) and all points with second coordinate negative 15/4.

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115.

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117.

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119.

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121.

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123.

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125.

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127.

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129.

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131.

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133.

The figure shows a straight vertical line drawn on the x y-coordinate plane. The x-axis of the plane runs from negative 7 to 7. The y-axis of the plane runs from negative 7 to 7. The vertical line goes through the points (3, 0), (3, 1), (3, 2) and all points with first coordinate 3.

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135.

$722, $850, $978

The figure shows a straight line drawn on the x y-coordinate plane. The x-axis of the plane runs from 0 to 1200 in increments of 100. The y-axis of the plane runs from 0 to 1000 in increments of 100. The straight line starts at the point (0, 594) and goes through the points (400, 722), (800, 850), and (1200, 978). The right end of the line has an arrow pointing up and to the right.

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137.

Answers will vary.

Section 4.3 Exercises

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139.

$(3, 0), (0, 3) (3, 0), (0, 3)$

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141.

$(5, 0), (0, −5) (5, 0), (0, −5)$

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143.

$(−2, 0), (0, −2) (−2, 0), (0, −2)$

Show solution

145.

$(−1, 0), (0, 1) (−1, 0), (0, 1)$

Show solution

147.

$(6, 0), (0, 3) (6, 0), (0, 3)$

Show solution

149.

$(0, 0) (0, 0)$

Show solution

151.

$(4, 0), (0, 4) (4, 0), (0, 4)$

Show solution

153.

$(−2, 0), (0, −2) (−2, 0), (0, −2)$

Show solution

155.

$(5, 0), (0, −5) (5, 0), (0, −5)$

Show solution

157.

$(−3, 0), (−3, 0),$

Show solution

159.

$(8, 0), (0, 4) (8, 0), (0, 4)$

Show solution

161.

$(2, 0), (0, 6) (2, 0), (0, 6)$

Show solution

163.

$(12, 0), (0, −4) (12, 0), (0, −4)$

Show solution

165.

$(2, 0), (0, −8) (2, 0), (0, −8)$

Show solution

167.

$(5, 0), (0, 2) (5, 0), (0, 2)$

Show solution

169.

$(4, 0), (0, −6) (4, 0), (0, −6)$

Show solution

171.

$(3, 0), (0, 1) (3, 0), (0, 1)$

Show solution

173.

$(−10, 0), (0, 2) (−10, 0), (0, 2)$

Show solution

175.

$(0, 0) (0, 0)$

Show solution

177.

$(0, 0) (0, 0)$

Show solution

179.

Show solution

181.

Show solution

183.

Show solution

185.

The figure shows a straight line on the x y- coordinate plane. The x- axis of the plane runs from negative 7 to 7. The y- axis of the planes runs from negative 7 to 7. The straight line goes through the points (negative 7, 4), (negative 6, 3), (negative 5, 2),(negative 4, 1), (negative 3, 0), (negative 2, negative 1), (negative 1, negative 2), (0, negative 3), (1, negative 4), (2, negative 5), (3, negative 6), and (4, negative 7).

Show solution

187.

Show solution

189.

Show solution

191.

Show solution

193.

Show solution

195.

Show solution

197.

Show solution

199.

Show solution

201.

Show solution

203.

Show solution

205.

ⓐ $(0, 1000), (15, 0) (0, 1000), (15, 0)$
ⓑ At $(0, 1000) (0, 1000)$ , he has been gone 0 hours and has 1000 miles left. At $(15, 0) (15, 0)$ , he has been gone 15 hours and has 0 miles left to go.

Show solution

207.

Answers will vary.

Show solution

209.

Answers will vary.

Section 4.4 Exercises

Show solution

211.

$\frac{1}{4} \frac{1}{4}$

Show solution

213.

$\frac{2}{3} \frac{2}{3}$

Show solution

215.

$\frac{−3}{2} = - \frac{3}{2} \frac{−3}{2} = - \frac{3}{2}$

Show solution

217.

$- \frac{2}{3} - \frac{2}{3}$

Show solution

219.

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 2, row 5 and the peg in column 5, row 3, forming a line.

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221.

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 4 and the peg in column 5, row 3, forming a line.

Show solution

223.

Show solution

225.

The figure shows a grid of evenly spaced pegs. There are 5 columns and 5 rows of pegs. A rubber band is stretched between the peg in column 1, row 2 and the peg in column 4, row 4, forming a line.

Show solution

227.

$\frac{2}{5} \frac{2}{5}$

Show solution

229.

$\frac{5}{4} \frac{5}{4}$

Show solution

231.

$- \frac{1}{3} - \frac{1}{3}$

Show solution

233.

$- \frac{3}{4} - \frac{3}{4}$

Show solution

235.

$\frac{3}{4} \frac{3}{4}$

Show solution

237.

$- \frac{5}{2} - \frac{5}{2}$

Show solution

239.

$- \frac{2}{3} - \frac{2}{3}$

Show solution

241.

$\frac{1}{4} \frac{1}{4}$

Show solution

243.

Show solution

245.

undefined

Show solution

247.

Show solution

249.

undefined

Show solution

251.

$\frac{5}{2} \frac{5}{2}$

Show solution

253.

$\frac{3}{4} \frac{3}{4}$

Show solution

255.

$- \frac{5}{2} - \frac{5}{2}$

Show solution

257.

$- \frac{8}{7} - \frac{8}{7}$

Show solution

259.

$\frac{7}{3} \frac{7}{3}$

Show solution

261.

$−1 −1$

Show solution

263.

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (1, negative 2) and (5, 1).

Show solution

265.

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (2, 5) and (5, 4).

Show solution

267.

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 3, 4) and (negative 1, 1).

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269.

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 1, negative 4) and intercepts the x-axis at (2, 0).

Show solution

271.

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line intercepts the y-axis at (0, 3) and passes through the point (5, 1).

Show solution

273.

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line intercepts the x-axis at (negative 2, 0) and passes through the point (2, 3).

Show solution

275.

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (negative 3, 3) and (negative 2, 5).

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277.

The graph shows the x y coordinate plane. The x and y-axes run from negative 12 to 12. A line passes through the points (1, 5) and (2, 2).

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279.

ⓐ $\frac{1}{3} \frac{1}{3}$ ⓑ 4 12 pitch or 4-in-12 pitch

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281.

$\frac{3}{50} \frac{3}{50}$ ; rise = 3, run = 50

Show solution

283.

ⓐ 288 inches (24 feet) ⓑ Models will vary.

Show solution

285.

When the slope is a positive number the line goes up from left to right. When the slope is a negative number the line goes down from left to right.

Show solution

287.

A vertical line has 0 run and since division by 0 is undefined the slope is undefined.

Section 4.5 Exercises

Show solution

289.

slope $m = 4 m = 4$ and y-intercept $(0, −2) (0, −2)$

Show solution

291.

slope $m = −3 m = −3$ and y-intercept $(0, 1) (0, 1)$

Show solution

293.

slope $m = - \frac{2}{5} m = - \frac{2}{5}$ and y-intercept $(0, 3) (0, 3)$

Show solution

295.

$−9; (0, 7) −9; (0, 7)$

Show solution

297.

$4; (0, −10) 4; (0, −10)$

Show solution

299.

$−4; (0, 8) −4; (0, 8)$

Show solution

301.

$- \frac{8}{3}; (0, 4) - \frac{8}{3}; (0, 4)$

Show solution

303.

$\frac{7}{3}; (0, −3) \frac{7}{3}; (0, −3)$

Show solution

305.

Show solution

307.

Show solution

309.

Show solution

311.

Show solution

313.

Show solution

315.

Show solution

317.

Show solution

319.

Show solution

321.

horizontal line

Show solution

323.

vertical line

Show solution

325.

slope–intercept

Show solution

327.

intercepts

Show solution

329.

slope–intercept

Show solution

331.

horizontal line

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333.

intercepts

Show solution

335.

slope–intercept

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337.

ⓐ $28
ⓑ $66.10
ⓒ The slope, 2.54, means that Randy’s payment, P, increases by $2.54 when the number of units of water he used, w, increases by 1. The P–intercept means that if the number units of water Randy used was 0, the payment would be $28.
ⓓ

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339.

ⓐ $15
ⓑ $143
ⓒ The slope, 0.32, means that the cost, C, increases by $0.32 when the number of miles driven, m, increases by 1. The C-intercept means that if Janelle drives 0 miles one day, the cost would be $15.
ⓓ

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341.

ⓐ $750
ⓑ $2418.60
ⓒ The slope, 0.09, means that Patel’s salary, S, increases by $0.09 for every $1 increase in his sales. The S-intercept means that when his sales are $0, his salary is $750.
ⓓ

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343.

ⓐ $2850
ⓑ $4950
ⓒ The slope, 42, means that the cost, C, increases by $42 for when the number of guests increases by 1. The C-intercept means that when the number of guests is 0, the cost would be $750.
ⓓ

Show solution

345.

parallel

Show solution

347.

parallel

Show solution

349.

not parallel

Show solution

351.

parallel

Show solution

353.

parallel

Show solution

355.

parallel

Show solution

357.

parallel

Show solution

359.

parallel

Show solution

361.

not parallel

Show solution

363.

not parallel

Show solution

365.

not parallel

Show solution

367.

not parallel

Show solution

369.

not parallel

Show solution

371.

perpendicular

Show solution

373.

perpendicular

Show solution

375.

not perpendicular

Show solution

377.

not perpendicular

Show solution

379.

perpendicular

Show solution

381.

perpendicular

Show solution

383.

ⓐ For every increase of one degree Fahrenheit, the number of chirps increases by four.
ⓑ There would be $−160 −160$ chirps when the Fahrenheit temperature is $0 ° 0 °$ . (Notice that this does not make sense; this model cannot be used for all possible temperatures.)

Show solution

385.

Answers will vary.

Section 4.6 Exercises

Show solution

387.

$y = 4 x + 1 y = 4 x + 1$

Show solution

389.

$y = 8 x - 6 y = 8 x - 6$

Show solution

391.

$y = − x + 7 y = − x + 7$

Show solution

393.

$y = −3 x - 1 y = −3 x - 1$

Show solution

395.

$y = \frac{1}{5} x - 5 y = \frac{1}{5} x - 5$

Show solution

397.

$y = - \frac{2}{3} x - 3 y = - \frac{2}{3} x - 3$

Show solution

399.

$y = 2 y = 2$

Show solution

401.

$y = −4 x y = −4 x$

Show solution

403.

$y = −2 x + 4 y = −2 x + 4$

Show solution

405.

$y = \frac{3}{4} x + 2 y = \frac{3}{4} x + 2$

Show solution

407.

$y = - \frac{3}{2} x - 1 y = - \frac{3}{2} x - 1$

Show solution

409.

$y = 6 y = 6$

Show solution

411.

$y = \frac{3}{8} x - 1 y = \frac{3}{8} x - 1$

Show solution

413.

$y = \frac{5}{6} x + 2 y = \frac{5}{6} x + 2$

Show solution

415.

$y = - \frac{3}{5} x + 1 y = - \frac{3}{5} x + 1$

Show solution

417.

$y = - \frac{1}{3} x - 11 y = - \frac{1}{3} x - 11$

Show solution

419.

$y = 4 y = 4$

Show solution

421.

$y = −7 y = −7$

Show solution

423.

$y = - \frac{5}{2} x - 22 y = - \frac{5}{2} x - 22$

Show solution

425.

$y = −4 x - 11 y = −4 x - 11$

Show solution

427.

$y = −8 y = −8$

Show solution

429.

$y = −4 x + 13 y = −4 x + 13$

Show solution

431.

$y = x + 5 y = x + 5$

Show solution

433.

$y = - \frac{1}{3} x - \frac{14}{3} y = - \frac{1}{3} x - \frac{14}{3}$

Show solution

435.

$y = 7 x + 22 y = 7 x + 22$

Show solution

437.

$y = - \frac{6}{7} x + \frac{4}{7} y = - \frac{6}{7} x + \frac{4}{7}$

Show solution

439.

$y = \frac{1}{5} x - 2 y = \frac{1}{5} x - 2$

Show solution

441.

$x = 4 x = 4$

Show solution

443.

$x = −2 x = −2$

Show solution

445.

$y = 2 y = 2$

Show solution

447.

$y = −3 y = −3$

Show solution

449.

$y = 4 x y = 4 x$

Show solution

451.

$y = \frac{1}{2} x + \frac{3}{2} y = \frac{1}{2} x + \frac{3}{2}$

Show solution

453.

$y = 5 y = 5$

Show solution

455.

$y = 3 x - 1 y = 3 x - 1$

Show solution

457.

$y = −3 x + 3 y = −3 x + 3$

Show solution

459.

$y = 2 x - 6 y = 2 x - 6$

Show solution

461.

$y = - \frac{2}{3} x + 5 y = - \frac{2}{3} x + 5$

Show solution

463.

$x = −3 x = −3$

Show solution

465.

$x = 4 x = 4$

Show solution

467.

$y = −4 y = −4$

Show solution

469.

$y = −1 y = −1$

Show solution

471.

$y = x y = x$

Show solution

473.

$y = - \frac{3}{2} x - 1 y = - \frac{3}{2} x - 1$

Show solution

475.

$y = - \frac{3}{4} x - \frac{1}{4} y = - \frac{3}{4} x - \frac{1}{4}$

Show solution

477.

$y = \frac{5}{4} x y = \frac{5}{4} x$

Show solution

479.

$x = −5 x = −5$

Show solution

481.

$y = 1 y = 1$

Show solution

483.

$y = x + 5 y = x + 5$

Show solution

485.

$y = \frac{5}{6} x + 2 y = \frac{5}{6} x + 2$

Show solution

487.

$y = - \frac{2}{3} x + 5 y = - \frac{2}{3} x + 5$

Show solution

489.

$y = - \frac{3}{5} x + 1 y = - \frac{3}{5} x + 1$

Show solution

491.

$y = 2 y = 2$

Show solution

493.

$y = x + 2 y = x + 2$

Show solution

495.

$x = −3 x = −3$

Show solution

497.

$y = - \frac{1}{3} x - \frac{14}{3} y = - \frac{1}{3} x - \frac{14}{3}$

Show solution

499.

$y = \frac{3}{4} x y = \frac{3}{4} x$

Show solution

501.

$y = 1.2 x + 5.2 y = 1.2 x + 5.2$

Show solution

503.

Answers will vary.

Section 4.7 Exercises

Show solution

505.

Show solution

507.

Show solution

509.

Show solution

511.

$y < 2 x - 4 y < 2 x - 4$

Show solution

513.

$y \leq - \frac{1}{3} x - 2 y \leq - \frac{1}{3} x - 2$

Show solution

515.

$x + y \geq 3 x + y \geq 3$

Show solution

517.

$x + 2 y \geq −2 x + 2 y \geq −2$

Show solution

519.

$2 x - y < 4 2 x - y < 4$

Show solution

521.

$4 x - 3 y > 12 4 x - 3 y > 12$

Show solution

523.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals three-fifths x plus 2 is plotted as a dashed line extending from the bottom left toward the top right. The region below the line is shaded.

Show solution

525.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative one-third x minus 2 is plotted as a solid line extending from the top left toward the bottom right. The region below the line is shaded.

Show solution

527.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x minus y equals negative 2 is plotted as a solid line extending from the bottom left toward the top right. The region below the line is shaded.

Show solution

529.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x plus 5 y equals negative 5 is plotted as a dashed line extending from the top left toward the bottom right. The region below the line is shaded.

Show solution

531.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line 4 x plus 2 y equals negative 8 is plotted as a solid line extending from the top left toward the bottom right. The region to the right of the line is shaded.

Show solution

533.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals x is plotted as a solid line extending from the bottom left toward the top right. The region above the line is shaded.

Show solution

535.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 3 x is plotted as a solid line extending from the top left toward the bottom right. The region to the left of the line is shaded.

Show solution

537.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 1 is plotted as a dashed horizontal line. The region below the line is shaded.

Show solution

539.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals 2 is plotted as a solid horizontal line. The region above the line is shaded.

Show solution

541.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x equals negative 2 is plotted as a dashed vertical line. The region to the right of the line is shaded.

Show solution

543.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x equals 4 is plotted as a solid vertical line. The region to the left of the line is shaded.

Show solution

545.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x minus y equals negative 3 is plotted as a dashed line extending from the bottom left toward the top right. The region above the line is shaded.

Show solution

547.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals five-fourths x is plotted as a solid line extending from the bottom left toward the top right. The region below the line is shaded.

Show solution

549.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 3 x minus 4 is plotted as a dashed line extending from the top left toward the bottom right. The region to the left of the line is shaded.

Show solution

551.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x equals negative 0 is plotted as a solid vertical line along the y-axis. The region to the right of the line is shaded.

Show solution

553.

ⓐ
ⓑ Answers will vary.

Review Exercises

Show solution

557.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (4, 3) is plotted and labeled "a". The point (negative 4, 3) is plotted and labeled "b". The point (negative 4, negative 3) is plotted and labeled "c". The point (4, negative 3) is plotted and labeled “d”.

Show solution

559.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (2, three halves) is plotted and labeled "a". The point (3, four thirds) is plotted and labeled "b". The point (one third, negative 4) is plotted and labeled "c". The point (one-half, negative 5) is plotted and labeled “d”.

Show solution

561.

Show solution

563.

a, b

Show solution

565.

$x x$	$y y$	$(x, y) (x, y)$
0	3	$(0, 3) (0, 3)$
4	1	(4, 1)
$−2 −2$	4	$(−2, 4) (−2, 4)$

Show solution

567.

$x x$	$y y$	$(x, y) (x, y)$
0	$−3 −3$	$(0, −3) (0, −3)$
2	0	$(2, 0) (2, 0)$
$−2 −2$	$−6 −6$	$(−2, −6) (−2, −6)$

Show solution

569.

Answers will vary.

Show solution

571.

Answers will vary.

Show solution

573.

ⓐ yes; yes ⓑ yes; no

Show solution

575.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals negative 3 x is plotted as an arrow extending from the top left toward the bottom right.

Show solution

577.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line x minus y equals 6 is plotted as an arrow extending from the bottom left toward the top right.

Show solution

579.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line 3 x minus 2 y equals 6 is plotted as an arrow extending from the bottom left toward the top right.

Show solution

581.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line x equals 3 is plotted as a vertical line.

Show solution

583.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals four-thirds x is plotted as an arrow extending from the bottom left toward the top right. The line y equals four-thirds is plotted as a horizontal line.

Show solution

585.

$(3, 0), (0, 3) (3, 0), (0, 3)$

Show solution

587.

$(−1, 0), (0, 1) (−1, 0), (0, 1)$

Show solution

589.

$(6, 0), (0, 4) (6, 0), (0, 4)$

Show solution

591.

$(0, 0) (0, 0)$

Show solution

593.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line x plus y equals negative 2 is plotted as an arrow extending from the top left toward the bottom right.

Show solution

595.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line 2 x minus y equals 5 is plotted as an arrow extending from the bottom left toward the top right.

Show solution

597.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals 2 x is plotted as an arrow extending from the bottom left toward the top right.

Show solution

599.

$\frac{4}{3} \frac{4}{3}$

Show solution

601.

$- \frac{2}{3} - \frac{2}{3}$

Show solution

603.

The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 5 and the point in column 3 row 2.

Show solution

605.

The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 2 row 2 and the point in column 3 row 3.

Show solution

607.

Show solution

609.

$- \frac{1}{2} - \frac{1}{2}$

Show solution

611.

undefined

Show solution

613.

Show solution

615.

$−6 −6$

Show solution

617.

$\frac{5}{2} \frac{5}{2}$

Show solution

619.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. A line passing through the points (negative 3, 4) and (0, 3) is plotted.

Show solution

621.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. A line passing through the points (0, 1) and (4, negative 2) is plotted.

Show solution

623.

$\frac{1}{10} \frac{1}{10}$

Show solution

625.

slope $m = - \frac{2}{3} m = - \frac{2}{3}$ and y-intercept $(0, 4) (0, 4)$

Show solution

627.

$\frac{5}{3}; (0, −6) \frac{5}{3}; (0, −6)$

Show solution

629.

$\frac{4}{5}; (0, - \frac{8}{5}) \frac{4}{5}; (0, - \frac{8}{5})$

Show solution

631.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line y equals negative x minus 1 is plotted from the top left to the bottom right.

Show solution

633.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The line 4 x minus 3 y equals 12 is plotted from the bottom left to the top right.

Show solution

635.

horizontal line

Show solution

637.

intercepts

Show solution

639.

plotting points

Show solution

641.

ⓐ −$250 ⓑ $450 ⓒ The slope, 35, means that Marjorie’s weekly profit, P, increases by $35 for each additional student lesson she teaches. The P–intercept means that when the number of lessons is 0, Marjorie loses $250. ⓓ