Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis

Be Prepared

4.1

2

4.2

16

4.3

5

4.4

−1

4.5

$y = \frac{12 - 3 x}{2}$

4.6

$- \frac{1}{2}$

4.7

$- \frac{1}{2}$

4.8

0, undefined

4.9

$−5, −5, 5$

4.10

$\frac{x + 1}{4}$

4.11

$\frac{7}{3}$

4.12

$y = \frac{12 - 2 x}{−3}$

4.13

$x = \frac{10}{3}$

4.14

$- \frac{2}{5} x + 6$

4.15

$x > 5$

4.16

x is less than 5.

4.17

7

Try It

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”.

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”.

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.

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.

4.5

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

4.6

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

4.7

a, c

4.8

b, c

4.9

b

4.10

a, b

4.11

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

4.12

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

4.13

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

4.14

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

4.15

Answers will vary.

4.16

Answers will vary.

4.17

Answers will vary.

4.18

Answers will vary.

4.19

ⓐ yes, yes ⓑ yes, yes

4.20

ⓐ no, no ⓑ yes, yes

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.

4.22

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.

4.24

4.25

4.26

4.27

4.28

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.

4.30

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.

4.32

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.

4.34

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).

4.36

4.37

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

4.38

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

4.39

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

4.40

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

4.41

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

4.42

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

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).

4.44

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).

4.46

4.47

4.48

4.49

$\frac{4}{3}$

4.50

$\frac{1}{4}$

4.51

$- \frac{2}{3}$

4.52

$- \frac{4}{3}$

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.

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.

4.55

4.56

4.57

$\frac{2}{5}$

4.58

$\frac{3}{4}$

4.59

$- \frac{4}{3}$

4.60

$- \frac{3}{5}$

4.61

$\frac{5}{4}$

4.62

$\frac{3}{2}$

4.63

undefined

4.64

0

4.65

1

4.66

1

4.67

$−1$

4.68

10

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).

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).

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).

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).

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).

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).

4.75

$\frac{7}{12}$

4.76

$\frac{5}{12}$

4.77

$- \frac{1}{36}$

4.78

$- \frac{1}{48}$

4.79

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

4.80

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

4.81

$\frac{2}{5}; (0, −1)$

4.82

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

4.83

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

4.84

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

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.

4.86

4.87

4.88

4.89

4.90

4.91

4.92

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.

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.

4.95

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

4.96

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

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.
ⓓ

4.98

ⓐ 40 degrees
ⓑ 65 degrees
ⓒ The slope, $\frac{1}{4}$ , 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 $40 °$ .
ⓓ

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
ⓓ

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.;
ⓓ

4.101

parallel

4.102

parallel

4.103

parallel

4.104

parallel

4.105

parallel

4.106

parallel

4.107

parallel

4.108

not parallel; same line

4.109

perpendicular

4.110

perpendicular

4.111

not perpendicular

4.112

not perpendicular

4.113

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

4.114

$y = − x - 3$

4.115

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

4.116

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

4.117

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

4.118

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

4.119

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

4.120

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

4.121

$y = 8$

4.122

$y = 4$

4.123

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

4.124

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

4.125

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

4.126

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

4.127

$x = 5$

4.128

$x = −4$

4.129

$y = 3 x - 10$

4.130

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

4.131

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

4.132

$y = −2 x + 16$

4.133

$y = −5$

4.134

$y = −1$

4.135

$x = −5$

4.136

$x = −4$

4.137

ⓐ yes ⓑ yes ⓒ yes ⓓ yes ⓔ no

4.138

ⓐ yes ⓑ yes ⓒ no ⓓ no ⓔ yes

4.139

$y \geq −2 x + 3$

4.140

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

4.141

$x - 4 y \leq 8$

4.142

$3 x - y \leq 6$

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.

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.

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.

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.

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.

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.

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.

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

1.

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”.

3.

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”.

5.

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”.

7.

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”.

9.

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

11.

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

13.

a, b

15.

a, c

17.

b, c

19.

a, b

21.

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

23.

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

25.

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

27.

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

29.

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

31.

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

33.

Answers will vary.

35.

Answers will vary.

37.

Answers will vary.

39.

Answers will vary.

41.

Answers will vary.

43.

Answers will vary.

45.

Answers will vary.

47.

Answers will vary.

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.

51.

Answers will vary.

53.

Answers will vary.

Section 4.2 Exercises

55.

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

57.

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

59.

61.

63.

65.

67.

69.

71.

73.

75.

77.

79.

81.

83.

85.

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.

89.

91.

93.

95.

97.

99.

101.

103.

105.

107.

109.

111.

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.

115.

117.

119.

121.

123.

125.

127.

129.

131.

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.

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.

137.

Answers will vary.

Section 4.3 Exercises

139.

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

141.

$(5, 0), (0, −5)$

143.

$(−2, 0), (0, −2)$

145.

$(−1, 0), (0, 1)$

147.

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

149.

$(0, 0)$

151.

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

153.

$(−2, 0), (0, −2)$

155.

$(5, 0), (0, −5)$

157.

$(−3, 0), (0, 3)$

159.

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

161.

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

163.

$(12, 0), (0, −4)$

165.

$(2, 0), (0, −8)$

167.

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

169.

$(4, 0), (0, −6)$

171.

$(−3, 0), (0, 1)$

173.

$(−10, 0), (0, 2)$

175.

$(0, 0)$

177.

$(0, 0)$

179.

181.

183.

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).

187.

189.

191.

193.

195.

197.

199.

201.

203.

205.

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

207.

Answers will vary.

209.

Answers will vary.

Section 4.4 Exercises

211.

$\frac{1}{4}$

213.

$\frac{2}{3}$

215.

$\frac{−3}{2} = - \frac{3}{2}$

217.

$- \frac{3}{4}$

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.

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.

223.

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.

227.

$\frac{2}{5}$

229.

$\frac{5}{4}$

231.

$- \frac{1}{3}$

233.

$- \frac{3}{4}$

235.

$\frac{3}{4}$

237.

$−3$

239.

$- \frac{2}{3}$

241.

$\frac{1}{4}$

243.

0

245.

undefined

247.

0

249.

undefined

251.

$\frac{5}{2}$

253.

$\frac{3}{4}$

255.

$- \frac{5}{2}$

257.

$- \frac{8}{7}$

259.

$\frac{7}{3}$

261.

$−1$

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).

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).

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).

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).

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).

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).

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).

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).

279.

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

281.

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

283.

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

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.

287.

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

Section 4.5 Exercises

289.

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

291.

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

293.

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

295.

$−9; (0, 7)$

297.

$4; (0, −10)$

299.

$−4; (0, 8)$

301.

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

303.

$\frac{7}{3}; (0, −3)$

305.

307.

309.

311.

313.

315.

317.

319.

321.

horizontal line

323.

vertical line

325.

slope–intercept

327.

intercepts

329.

slope–intercept

331.

horizontal line

333.

intercepts

335.

slope–intercept

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.
ⓓ

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.
ⓓ

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.
ⓓ

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.
ⓓ

345.

parallel

347.

parallel

349.

not parallel

351.

parallel

353.

parallel

355.

parallel

357.

parallel

359.

parallel

361.

not parallel

363.

not parallel

365.

not parallel

367.

not parallel

369.

not parallel

371.

perpendicular

373.

perpendicular

375.

not perpendicular

377.

not perpendicular

379.

perpendicular

381.

perpendicular

383.

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

385.

Answers will vary.

Section 4.6 Exercises

387.

$y = 4 x + 1$

389.

$y = 8 x - 6$

391.

$y = − x + 7$

393.

$y = −3 x - 1$

395.

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

397.

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

399.

$y = 2$

401.

$y = −4 x$

403.

$y = −2 x + 4$

405.

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

407.

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

409.

$y = 6$

411.

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

413.

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

415.

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

417.

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

419.

$y = 4$

421.

$y = −7$

423.

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

425.

$y = −4 x - 11$

427.

$y = −8$

429.

$y = −4 x + 13$

431.

$y = x + 5$

433.

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

435.

$y = 7 x + 22$

437.

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

439.

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

441.

$x = 4$

443.

$x = −2$

445.

$y = 2$

447.

$y = −3$

449.

$y = 4 x$

451.

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

453.

$y = 5$

455.

$y = 3 x - 1$

457.

$y = −3 x + 3$

459.

$y = 2 x - 6$

461.

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

463.

$x = −3$

465.

$x = 4$

467.

$y = −4$

469.

$y = −1$

471.

$y = x$

473.

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

475.

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

477.

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

479.

$x = −5$

481.

$y = 1$

483.

$y = x + 5$

485.

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

487.

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

489.

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

491.

$y = 2$

493.

$y = 2 x + 4$

495.

$x = −3$

497.

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

499.

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

501.

$y = 1.2 x + 5.2$

503.

Answers will vary.

Section 4.7 Exercises

505.

507.

509.

511.

$y < 2 x - 4$

513.

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

515.

$x + y \geq 3$

517.

$x + 2 y \leq −2$

519.

$2 x - y < 4$

521.

$4 x - 3 y > 12$

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

553.

ⓐ
ⓑ Answers will vary.

Review Exercises

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”.

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”.

561.

563.

a, b

565.

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

567.

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

569.

Answers will vary.

571.

Answers will vary.

573.

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.

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.

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.

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.

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.

585.

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

587.

$(−1, 0), (0, 1)$

589.

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

591.

$(0, 0)$

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.

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.

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.

599.

$\frac{4}{3}$

601.

$- \frac{2}{3}$

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.

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.

607.

1

609.

$- \frac{1}{2}$

611.

undefined

613.

0

615.

$−6$

617.

$\frac{5}{2}$

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.

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.

623.

$\frac{1}{10}$

625.

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

627.

$\frac{5}{3}; (0, −6)$

629.

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

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.

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.

635.

horizontal line

637.

intercepts

639.

plotting points

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. ⓓ