49. Arithmetic Sequences Use the arithmetic sequence 10, 15, 20, 25, …

    1. Find the common difference of the sequence.
    2. Let x = the term number, and let y = the corresponding term of the sequence. Graph the ordered pairs (x, y) for the first eight terms of the sequence. Draw a line through the points.
    3. Reasoning How is the slope of a line from part (b) related to the common difference of the sequence?

C Challenge

Do the points in each set lie on the same line? Explain your answer.

50. A ( 1 , 3 ) , B ( 4 , 2 ) , C ( − 2 , 4 ) eh open 1 comma 3 close comma b open 4 comma 2 close comma c open negative 2 comma 4 close
51. G ( 3 , 5 ) , H ( − 1 , 3 ) , I ( 7 , 7 ) g open 3 comma 5 close comma h open negative 1 comma 3 close comma i open 7 comma 7 close
52. D ( − 2 , 3 ) , E ( 0 , − 1 ) , F ( 2 , 1 ) d open negative 2 comma 3 close comma e open 0 comma negative 1 close comma f open 2 comma 1 close
53. P ( 4 , 2 ) , Q ( − 3 , 2 ) , R ( 2 , 5 ) p open 4 comma 2 close comma q open negative 3 comma 2 close comma r open 2 comma 5 close
54. G ( 1 , − 2 ) , H ( − 1 , − 5 ) , I ( 5 , 4 ) g open 1 comma negative 2 close comma h open negative 1 comma negative 5 close comma i open 5 comma 4 close
55. S ( − 3 , 4 ) , T ( 0 , 2 ) , X ( − 3 , 0 ) s open negative 3 comma 4 close comma t open 0 comma 2 close comma x open negative 3 comma 0 close

Find the slope of the line that passes through each pair of points.

56. ( a , − b ) , ( − a , − b ) open eh comma negative b close comma open negative eh comma negative b close
57. ( − m , n ) , ( 3 m , − n ) open negative m comma n close comma open 3 m comma negative n close
58. ( 2 a , b ) , ( c , 2 d ) open 2 eh comma b close comma open c comma 2 d close

Standardized Test Prep

SAT/ACT

59. A line has slope 4 3 . 4 thirds , .  Through which two points could this line pass?

    1. (24, 19), (8, 10)
    2. (10, 8), (16, 0)
    3. (28, 10), (22, 2)
    4. (4, 20), (0, 17)

60. Let the domain of the function f ( x ) = 1 5 x − 12 f open x close equals , 1 fifth , x minus 12  be { − 5 , 0 , 10 } . left brace negative 5 comma 0 comma 10 right brace .  What is the range?

    6. { − 5 , 0 , 10 } the set negative 5 comma 0 comma 10 end set
    7. { 0 , 12 , 13 } the set 0 comma 12 comma 13 end set
    8. { − 13 , − 12 , − 11 } the set negative 13 comma negative 12 comma negative 11 end set
    9. { − 13 , − 12 , − 10 } the set negative 13 comma negative 12 comma negative 10 end set

Extended Response

61. The perimeter of the rectangle below is less than 30 in. and greater than 20 in.

    

    

    1. What is an inequality that represents the situation?
    2. What is a graph that shows all the possible values of x?
    3. What is a graph that shows all the possible perimeters of the triangle?

Mixed Review

See Lesson 4-7.

Find the second, fourth, and tenth terms of each sequence.

62. A ( n ) = 3 + ( n − 1 ) ( 2 ) eh open n close equals 3 plus open n minus 1 close open 2 close
63. A ( n ) = − 5 + ( n − 1 ) ( 6 ) eh open n close equals negative 5 plus open n minus 1 close open 6 close
64. A ( n ) = 12 + ( n − 1 ) ( 3 ) eh open n close equals 12 plus open n minus 1 close open 3 close

See Lesson 3-8.

Find each union or intersection. Let A = { 1 , 2 , 3 , 4 } , B = { 2 , 4 , 6 , 8 , 10 } , eh equals left brace 1 comma 2 comma 3 comma 4 right brace comma b equals left brace 2 comma 4 comma 6 comma 8 comma 10 right brace comma  and C = { 3 , 5 , 7 , 8 } . c equals left brace 3 comma 5 comma 7 comma 8 right brace .

65. A ∩ B eh intersection b
66. A ∩ C eh intersection c
67. B ∩ C b intersection c
68. B ∪ C b union c
69. A ∪ C eh union c

Get Ready! To prepare for Lesson 5-2, do Exercises 70–74.

See Lesson 2-7.

Solve each proportion.

70. 5 8 = x 12 5 eighths , equals , x over 12
71. − 4 9 = n − 45 negative 4 over 9 , equals , n over negative 45
72. y 3 = 25 15 y over 3 , equals , 25 over 15
73. 7 n = − 35 50 7 over n , equals . negative 35 over 50
74. 14 18 = 63 n 14 over 18 , equals , 63 over n

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