12.4.11: Chapter 11

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May 28, 2023
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- 12.4.10: Chapter 10
- Back Matter

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Be Prepared

11.1

$2$

11.2

$16$

11.3

$5$

11.4

$- 1$

11.5

$y = \frac{20 - 5 x}{2}$

11.6

$- 9$

11.7

$- 4$

11.8

$y -axis$

11.9

11.10

$- \frac{1}{2}$

11.11

$0, undefined$

11.12

$- 5, - 5, 5$

Try It

11.1

ⓐ 1C
ⓑ Engineering Building

11.2

ⓐ 1A
ⓑ Library

11.3 $This answer graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. There are two labeled points: the first is ordered pair (5, 2), and the second is (2, 5)$

11.4 $This answer graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. There are two labeled points: the first is ordered pair (2, 4), and the second is (4, 2)$

11.5

(a) Quadrant II, (b) Quadrant III, (c) Quadrant IV, (d) Quadrant II

$The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point “ordered pair -2, 1” is labeled “a”. The point “ordered pair -3, 1” is labeled “b”. The point “ordered pair 4, -4 is labeled “c”. The point “ordered pair -4, 3/2” is labeled “d”.$

11.6

(a) Quadrant II, (b) Quadrant II, (c) Quadrant IV, (d) Quadrant II

$This image is an answer graph and shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point “ordered pair -4, 1” is labeled “a”. The point “ordered pair -2, 3” is labeled “b”. The point “ordered pair 2, -5” is labeled “c”. The point “ordered pair -3, 5/2” is labeled “d”.$

11.7 $This image is an answer graph and shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point “ordered pair 4, -3” is labeled “a”. The point “ordered pair 4, 3” is labeled “b”. The point “ordered pair -4, -3” is labeled “c”. The point “ordered pair -4, 3” is labeled “d”.$

11.8 $This image is an answer graph and shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point “ordered pair -1, -4” is labeled “a”. The point “ordered pair 1, 4” is labeled “b”. The point “ordered pair 1, -4” is labeled “c”. The point “ordered pair -1, -4” is labeled “d”.$

11.9 $This image is an answer graph and shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point for ordered pair 4, 0 is plotted. The point for ordered pair -2, 0 is plotted. The point for ordered pair 0,0 is plotted. The point for ordered pair 0, 2 is plotted. The point for ordered pair 0,-3 is plotted.$

11.10 $This image is an answer graph and shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point for ordered pair -5, 0 is plotted. The point for ordered pair 3, 0 is plotted. The point for ordered pair 0,0 is plotted. The point for ordered pair 0, -1 is plotted. The point for ordered pair 0,4 is plotted.$

11.11

A: (5,1)
B: (−2,4)
C: (−5,−1)
D: (3,−2)

11.12

A: (4,2)
B: (−2,3)
C: (−4,−4)
D: (3,−5)

11.13

A: (4,0)
B: (0,3)
C: (−3,0)
D: (0,−5)

11.14

A: (−3,0)
B: (0,−3)
C: (5,0)
D: (0,2)

11.15

ⓐ, ⓒ

11.16

ⓑ, ⓒ

11.17

ⓑ

11.18

ⓐ, ⓑ

11.19

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

11.20

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

11.21

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

11.22

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

11.23

Answers will vary.

11.24

Answers will vary.

11.25

Answers will vary.

11.26

Answers will vary.

11.27

Answers will vary.

11.28

Answers will vary.

11.29

ⓐ yes ⓑ yes
ⓐ no ⓑ no
ⓐ no ⓑ no
ⓐ yes ⓑ yes

11.30 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 0” and “ordered pair 4, -4”.$

11.31 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 0” and “ordered pair 1, -4”.$

11.32 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, -1” and “ordered pair 3, 0”.$

11.33 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 2” and “ordered pair -12, 0”.$

11.34 $This answer graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. The equation x plus y equals -2 is shown. A line passes through the intercepts with coordinates 0, –2 and –2, 0.$

11.35 $The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points “ordered pair 6, 0” and “ordered pair 0, -6”.$

11.36 $The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through three labeled points, “ordered pair -1, 2”, “ordered pair 0, -1”, and ordered pair 1, -4”. The line is labeled 3 x + y = -1.$

11.37 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair -1, 4” and “ordered pair 0, -3”.$

11.38 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A vertical line passes through the points “ordered pair 5, 0” and “ordered pair 5, 1”.$

11.39 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A vertical line passes through the points “ordered pair 5, 0” and “ordered pair 5, 1”.$

11.40 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A horizontal line passes through the points “ordered pair 0, -4” and “ordered pair 1, -4”.$

11.41 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A horizontal line passes through the points “ordered pair 0, 3” and “ordered pair 1, 3”.$

11.42 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A horizontal line passes through “ordered pair 0, -4” and “ordered pair 1, -4” . A second line passes through “ordered pair 0, 0” and “ordered pair 1, -4” . The two lines intersect at “ordered pair 1, -4”.$

11.43 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A horizontal line passes through “ordered pair 0, 3” and “ordered pair 1, 3” . A second line passes through “ordered pair 0, 0” and “ordered pair 1, 3” . The two lines intersect at “ordered pair 1, 3”.$

11.44

x-intercept (2,0): y-intercept (0,−2)

11.45

x-intercept (3,0); y-intercept (0,2)

11.46

$(4, 0)$ and $(0, 12)$

11.47

$(8, 0)$ and $(0, 2)$

11.48

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

11.49

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

11.50 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, -2” and “ordered pair 4, 0”.$

11.51 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 2” and “ordered pair -6, 0”.$

11.52 $The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points “ordered pair 0, -5” and “ordered pair 2, 0”.$

11.53 $The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. A line passes through the points “ordered pair 0, -3” and “ordered pair 4, 0”.$

11.54 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 0” and “ordered pair 1, 3”.$

11.55 $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 0” and “ordered pair 1, -1”.$

11.56

ⓐ intercepts
ⓑ horizontal line
ⓒ plotting points
ⓓ vertical line

11.57

ⓐ vertical line
ⓑ plotting points
ⓒ horizontal line
ⓓ intercepts

11.58

$\frac{4}{3}$

11.59

$\frac{1}{4}$

11.60

$- \frac{2}{3}$

11.61

$- \frac{4}{3}$

11.62 $The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style triangle connecting three of the three points at column 2 row 3, column 2 row 4,and column 5 row 3.$

11.63 $The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style triangle connecting three of the three points at column 1 row 1, column 1 row 4,and column 3 row 1.$

11.64 $The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style triangle connecting three of the three points at column 2 row 3, column 2 row 5,and column 3 row 5.$

11.65 $The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style triangle connecting three of the three points at column 1 row 1, column 1 row 2,and column 4 row 2.$

11.66

$\frac{2}{5}$

11.67

$\frac{3}{4}$

11.68

$- \frac{4}{3}$

11.69

$- \frac{3}{5}$

11.70

$\frac{5}{4}$

11.71

$\frac{3}{2}$

11.72

undefined

11.73

11.74

11.75

11.76

−1

11.77

11.78 $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from -12 to 12. A line passes through the points “ordered pair -2, 3” and “ordered pair 8, 6”.$

11.79 $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from -12 to 12. A line passes through the points “ordered pair -2, 3” and “ordered pair 2, 4”.$

11.80 $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from -12 to 12. A line passes through the points “ordered pair 0, 4” and “ordered pair 4, -6”.$

11.81 $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from -12 to 12. A line passes through the points “ordered pair -3, 0” and “ordered pair 8, -8”.$

11.82 $The graph shows the x y-coordinate plane. The x-axis runs from -7 to 7. The y-axis runs from -7 to 7. A line passes through the points “ordered pair -2, 1” and “ordered pair 0, 7”.$

11.83 $The graph shows the x y-coordinate plane. The x-axis runs from -7 to 7. The y-axis runs from -7 to 7. A line passes through the points “ordered pair 0, 6” and “ordered pair 0, 3”.$

11.84

$\frac{7}{12}$

11.85

$\frac{5}{12}$

11.86

$- \frac{1}{36}$

11.87

$- \frac{1}{48}$

Section 11.1 Exercises

1. $The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point “ordered pair 3, 2” is labeled$

3. $The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point “ordered pair 1, 5” is labeled$

5. $The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point “ordered pair 1, 4” is labeled. The point “ordered pair 4, 1” is labeled.$

7. $The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point “ordered pair 3, 4” is labeled. The point “ordered pair 4, 3” is labeled.$

9. $The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The quadrants are labeled I, II, III, and IV. The point (-1, 1) is labeled a, the point (-2, -1) is labeled b. The point (1, -4) is labeled c, and the point (3, 7/2) is labeled d.$

11. $The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point (3, -2) is labeled a, the point (-3, 2) is labeled b. The point (-3, -2) is labeled c, and the point (3, 2) is labeled d.$

13. $The graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The point (-2, 0) is labeled a, the point (-3, 0) is labeled b. The point (0, 4) is labeled c, and the point (0, 2) is labeled d.$

15.

C(1, -3) D(4, 3)

17.

S(-2, 4) T(-4, -2)

19.

C(0, -1) D(-1, 0)

21.

ⓐ, ⓑ

23.

ⓐ, ⓒ

25.

ⓑ, ⓒ

27.

ⓐ, ⓑ

29.

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

31.

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

33.

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

35.

ⓐ $This figure shows points plot on the x y coordinate plane. There are 7 points graphed without labeled at approximately the points “ordered pair 0, 7”, “ordered pair 2, 11”, “ordered pair 4, 15”, “ordered pair 6, 16”, “ordered pair 8, 19”, “ordered pair 10, 20”, “ordered pair 12, 21”.$
ⓑ Age and weight are only positive.

37.

Answers may vary.

Section 11.2 Exercises

39.

ⓐ yes ⓑ yes
ⓐ no ⓑ no
ⓐ yes ⓑ yes
ⓐ no ⓑno

41.

ⓐ yes ⓑ yes
ⓐ yes ⓑ yes
ⓐ yes ⓑ yes
ⓐ no ⓑno

43. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, -1” and “ordered pair 1/3, 0”.$

45. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 4” and “ordered pair 1, 0”.$

47. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 2” and “ordered pair 2, 4”.$

49. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, -3” and “ordered pair 1, -4”.$

51. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 0” and “ordered pair 2, 4”.$

53. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 0” and “ordered pair 1, -4”.$

55. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 2” and “ordered pair 4, 4”.$

57. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 5” and “ordered pair 4, 2”.$

59. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 1” and “ordered pair 8, -2”.$

61. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 2” and “ordered pair 4, -4”.$

63. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 6” and “ordered pair 6, 0”.$

65. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, -3” and “ordered pair -3, 0”.$

67. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, -2” and “ordered pair 2, 0”.$

69. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 1” and “ordered pair 8, 8”.$

71. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair -4, 0” and “ordered pair 0, 4”.$

73. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair -5, 0” and “ordered pair 0, -5”.$

75. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 4, -4” and “ordered pair 0, 8”.$

77. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, -3” and “ordered pair 2, -7”.$

79. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 4” and “ordered pair 6, 0”.$

81. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 2” and “ordered pair 6, 0”.$

83. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A vertical line passes through the points “ordered pair 4, 0” and “ordered pair 4, 1”.$

85. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A vertical line passes through the points “ordered pair -2, 0” and “ordered pair -2, 1”.$

87. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A horizontal line passes through the points “ordered pair 0, 3” and “ordered pair 1, 3”.$

89. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A horizontal line passes through the points “ordered pair 0, -5” and “ordered pair 1, -5”.$

91. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A vertical line passes through the points “ordered pair 7 over 3, 0” and “ordered pair 7 over 3 , 1”.$

93. $...$

95. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A horizontal line passes through “ordered pair 0, 2” and “ordered pair 1, 2” . A second line passes through “ordered pair 0, 0” and “ordered pair 1, 2” . The two lines intersect at “ordered pair 1, 2”.$

97. $...$

99. $...$

101.

$...$

103.

$...$

105.

$...$

107.

$...$

109.

$...$

111.

$...$

113. $The graph shows the x y-coordinate plane. The x-axis runs from 0 to 1000. The y-axis runs from 0 to 1200. A line passes through the points “ordered pair 0, 594” and “ordered pair 800, 850”.$

$722, $850, $978

115.

Answers will vary.

Section 11.3 Exercises

117.

(3,0),(0,3)

119.

(5,0),(0,−5)

121.

(−2,0),(0,−2)

123.

(−1,0),(0,1)

125.

(0,0)

127.

(4,0),(0,4)

129.

(−2,0),(0,−2)

131.

(5,0),(0,−5)

133.

(−3,0),(0,3)

135.

(8,0),(0,4)

137.

(2,0),(0,6)

139.

(12,0),(0,−4)

141.

(2,0),(0,−8)

143.

(5,0),(0,2)

145.

(4,0),(0,−6)

147.

(3,0),(0,−1)

149.

(−10,0),(0,2)

151.

(0,0)

153.

(0,0)

155. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 2” and “ordered pair -10, 0”.$

157. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 2” and “ordered pair 4, 0”.$

159. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 2” and “ordered pair 2, 0”.$

161. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 3” and “ordered pair 3, 0”.$

163. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, -1” and “ordered pair 1, 0”.$

165. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 4” and “ordered pair -4, 0”.$

167. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 4” and “ordered pair 1, 0”.$

169. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 6” and “ordered pair -2, 0”.$

171.

$The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 3” and “ordered pair 6, 0”.$

173. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, -3” and “ordered pair 2, 0”.$

175. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 4” and “ordered pair -10, 0”.$

177. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 0” and “ordered pair 2, -4”.$

179. $The graph shows the x y-coordinate plane. The x and y-axis each run from -12 to 12. A line passes through the points “ordered pair 0, 0” and “ordered pair 2, 2”.$

181.

vertical line

183.

horizontal line

185.

plotting points

187.

intercepts

189.

plotting points

191.

horizontal line

193.

intercepts

195.

plotting points

197.

ⓐ (0,1,000),(15,0). ⓑ At (0,1,000) he left Chicago 0 hours ago and has 1,000 miles left to drive. At (15,0) he left Chicago 15 hours ago and has 0 miles left to drive.

199.

Answers will vary.

201.

Answers will vary.

Section 11.4 Exercises

203.

$\frac{1}{4}$

205.

$- \frac{3}{2}$

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

209. $The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 4 and the point in column 5 row 3.$

211. $The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 4 and the point in column 3 row 5.$

213. $The figure shows a grid of evenly spaced dots. There are 5 rows and 5 columns. There is a rubber band style loop connecting the point in column 1 row 2 and the point in column 4 row 4.$

215.

$\frac{2}{5}$

217.

$\frac{5}{4}$

219.

$- \frac{1}{3}$

221.

$- \frac{3}{4}$

223.

$\frac{3}{4}$

225.

$- \frac{5}{2}$

227.

$- \frac{2}{3}$

229.

$\frac{1}{4}$

231.

233.

undefined

235.

237.

undefined

239.

$\frac{5}{2}$

241.

$\frac{3}{4}$

243.

$- \frac{5}{2}$

245.

$- \frac{8}{5}$

247.

$\frac{7}{3}$

249.

−1

251. $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair 5, 1” and “ordered pair 1, -2”$

253. $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair 2, 5” and “ordered pair 5, 4”.$

255. $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair -3, 4” and “ordered pair -1, 1”.$

257. $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair 2,0” and “ordered pair -1, -4”.$

259. $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair 0, 3” and “ordered pair 5, 1”.$

261. $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair -2,0” and “ordered pair 2, 3”.$

263. $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair -3, 3” and “ordered pair -2, 5”.$

265. $The graph shows the x y-coordinate plane. The x-axis runs from -12 to 12. The y-axis runs from 12 to -12. A line passes through the points “ordered pair 1, 5” and “ordered pair 2, 2”.$

267.

$\frac{1}{3}$

269.

ⓐ $\frac{3}{50}$ ⓑ $rise = 3; run = 50$

271.

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

273.

Answers will vary.

275.

Answers will vary.

Review Exercises

277. $The graph shows the x y-coordinate plane. The x-axis runs from -6 to 6. The y-axis runs from 6 to -6. The points “ordered pair 1,3” and “ordered pair 3,1” are plotted.$

279.

ⓐ III
ⓑ II
ⓒ IV
ⓐ I

$147ce678b2f14ce488dddb682547e51d87ca5790$

281.

ⓐ (5,3)
ⓑ (2,−1)
ⓒ (−3,−2)
ⓓ (−1,4)

283.

ⓐ (2,0)
ⓑ (0,−5)
ⓒ (−4,0)
ⓓ (0,3)

285.

ⓑ,ⓒ

287.

$x$	$y$	$(x, y)$
$0$	$−1$	$(0, −1)$
$1$	$3$	$(1, 3)$
$−2$	$−9$	$(−2, −9)$

289.

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

291.

Answers will vary.

293.

Answers will vary.

295.

ⓐ yes ⓑ yes
ⓐ no ⓑ no
ⓐ yes ⓑ yes
ⓐ yes ⓑ yes

297. $The graph shows the x y-coordinate plane. Each axis runs from -6 to 6. A line passes through the points “ordered pair 1, 1” and “ordered pair 0, -3”.$

299. $The graph shows the x y-coordinate plane. Each axis runs from -6 to 6. A line passes through the points “ordered pair 1, 5” and “ordered pair 0, 7”.$

301. $The graph shows the x y-coordinate plane. Each axis runs from -6 to 6. A vertical line passes through the point “ordered pair 0, 3”.$

303.

(0,3) (3,0)

305.

(−1,0) (0,1)

307.

(0,0)

309. $This answer graph shows the x y-coordinate plane. The x and y-axis each run from -6 to 6. The equation x plus y equals -2 is shown. A line passes through the intercepts with coordinates 0, –2 and –2, 0.$

311.

horizontal line

313.

intercepts

315.

plotting points

317.

$\frac{4}{3}$

319.

$- \frac{2}{3}$

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

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

325.

327.

$- \frac{1}{2}$

329.

undefined

331.

333.

−4

335.

$\frac{1}{2}$

337. $The graph shows the x y-coordinate plane. The x-axis runs from -6 to 6. The y-axis runs from -4 to 2. A line passes through the points “ordered pair -3, 4” and “ordered pair 1, 3”.$

Practice Test

339. $The graph shows the x y-coordinate plane. The axes extend from -6 to 6. a is plotted at 2, 5, b at -1, -3, c at -4, 0, d at 3, -5, and e at -2,1.$

341.

(4,0), (0,−2)

343.

no; 1 + 4 · 3 ≠ 12

345.

$x$	$y$	$(x, y)$
$0$	$8$	$(0, 8)$
$2$	$0$	$(2, 0)$
$3$	$−4$	$(3, −4)$

347. $The graph shows the x y-coordinate plane. The x-axis runs from -6 to 6. The y-axis runs from -6 to 6. A line passes through the points “ordered pair 0, -2” and “ordered pair -3, 0”.$

349.

$- \frac{5}{2}$

351.

353.

$\frac{1}{50}$

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