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12.4.11: Chapter 11

  • Page ID
    119032
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    Be Prepared

    11.1

    2 2

    11.2

    16 16

    11.3

    5 5

    11.4

    1 1

    11.5

    y = 20 5 x 2 y = 20 5 x 2

    11.6

    9 9

    11.7

    4 4

    11.8

    y -axis y -axis

    11.9

    b

    11.10

    1 2 1 2

    11.11

    0, undefined 0, undefined

    11.12

    5 , 5 , 5 5 , 5 , 5

    Try It

    11.1
    1. 1C
    2. Engineering Building
    11.2
    1. 1A
    2. Library
    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”.
    11.11
    1. A: (5,1)
    2. B: (−2,4)
    3. C: (−5,−1)
    4. D: (3,−2)
    11.12
    1. A: (4,2)
    2. B: (−2,3)
    3. C: (−4,−4)
    4. D: (3,−5)
    11.13
    1. A: (4,0)
    2. B: (0,3)
    3. C: (−3,0)
    4. D: (0,−5)
    11.14
    1. A: (−3,0)
    2. B: (0,−3)
    3. C: (5,0)
    4. D: (0,2)
    11.15

    ,

    11.16

    ,

    11.17

    11.18

    ,

    11.19
    y=3x1y=3x1
    xx yy (x,y)(x,y)
    00 −1−1 (0,−1)(0,−1)
    −1−1 −4−4 (−1,−4)(−1,−4)
    22 55 (2,5)(2,5)
    11.20
    y=6x+1y=6x+1
    xx yy (x,y)(x,y)
    00 11 (0,1)(0,1)
    11 77 (1,7)(1,7)
    −2−2 −11−11 (−2,−11)(−2,−11)
    11.21
    2x5y=202x5y=20
    xx yy (x,y)(x,y)
    00 −4−4 (0,−4)(0,−4)
    1010 00 (10,0)(10,0)
    −5−5 −6−6 (−5,−6)(−5,−6)
    11.22
    3x4y=123x4y=12
    xx yy (x,y)(x,y)
    00 −3−3 (0,−3)(0,−3)
    44 00 (4,0)(4,0)
    −4−4 −6−6 (−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
    1. yes yes
    2. no no
    3. no no
    4. yes yes
    11.44

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

    11.45

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

    11.46

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

    11.47

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

    11.48

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

    11.49

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

    11.56
    1. intercepts
    2. horizontal line
    3. plotting points
    4. vertical line
    11.57
    1. vertical line
    2. plotting points
    3. horizontal line
    4. intercepts
    11.58

    4 3 4 3

    11.59

    1 4 1 4

    11.60

    2 3 2 3

    11.61

    4 3 4 3

    11.66

    2 5 2 5

    11.67

    3 4 3 4

    11.68

    4 3 4 3

    11.69

    3 5 3 5

    11.70

    5 4 5 4

    11.71

    3 2 3 2

    11.72

    undefined

    11.76

    −1

    11.77

    10

    11.84

    7 12 7 12

    11.85

    5 12 5 12

    11.86

    1 36 1 36

    11.87

    1 48 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.
    xx yy (x,y)(x,y)
    −1−1 −6−6 (−1,−6)(−1,−6)
    00 −4−4 (0,−4)(0,−4)
    22 00 (2,0)(2,0)
    31.
    xx yy (x,y)(x,y)
    −2−2 77 (−2,7)(−2,7)
    00 55 (0,5)(0,5)
    33 22 (3,2)(3,2)
    33.
    xx yy (x,y)(x,y)
    −2−2 11 (−2,1)(−2,1)
    00 −2−2 (0,−2)(0,−2)
    22 −5−5 (2,−5)(2,−5)
    35.
    1. 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”.
    2. Age and weight are only positive.
    37.

    Answers may vary.

    Section 11.2 Exercises

    39.
    1. yes yes
    2. no no
    3. yes yes
    4. no no
    41.
    1. yes yes
    2. yes yes
    3. yes yes
    4. 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.

    1 4 1 4

    205.

    3 2 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.

    2 5 2 5

    217.

    5 4 5 4

    219.

    1 3 1 3

    221.

    3 4 3 4

    223.

    3 4 3 4

    225.

    5 2 5 2

    227.

    2 3 2 3

    229.

    1 4 1 4

    231.

    0

    233.

    undefined

    235.

    0

    237.

    undefined

    239.

    5 2 5 2

    241.

    3 4 3 4

    243.

    5 2 5 2

    245.

    8 5 8 5

    247.

    7 3 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.

    1 3 1 3

    269.

    3 50 3 50 rise = 3 ; run = 50 rise = 3 ; run = 50

    271.
    1. 288 inches (24 feet)
    2. 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.
    1. III
    2. II
    3. IV
    4. I
    147ce678b2f14ce488dddb682547e51d87ca5790
    281.
    1. (5,3)
    2. (2,−1)
    3. (−3,−2)
    4. (−1,4)
    283.
    1. (2,0)
    2. (0,−5)
    3. (−4,0)
    4. (0,3)
    285.

    ,

    287.
    xx yy (x,y)(x,y)
    00 −1−1 (0,−1)(0,−1)
    11 33 (1,3)(1,3)
    −2−2 −9−9 (−2,−9)(−2,−9)
    289.
    xx yy (x,y)(x,y)
    55 00 (5,0)(5,0)
    11 22 (1,2)(1,2)
    −1−1 33 (−1,3)(−1,3)
    291.

    Answers will vary.

    293.

    Answers will vary.

    295.
    1. yes yes
    2. no no
    3. yes yes
    4. 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.

    4 3 4 3

    319.

    2 3 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.

    1

    327.

    1 2 1 2

    329.

    undefined

    331.

    0

    333.

    −4

    335.

    1 2 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.
    xx yy (x,y)(x,y)
    00 88 (0,8)(0,8)
    22 00 (2,0)(2,0)
    33 −4−4 (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.

    5 2 5 2

    351.

    0

    353.

    1 50 1 50


    12.4.11: Chapter 11 is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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