246 Chapter 3 Graphing Linear Equations in Two Variables For Exercises 33–54, find the slope of the line that passes through the two points. (See Examples 2–5.) 33. 34. 35. 10, 42 and 13, 02 12, 32 and 11, 02 1 4 3 13, 42 and 11, 52 11, 52 and 14, 22 16, 12 and 12, 32 36. 37. 38. 39. 40. 41. 15, 32 and 12, 32 Zero 10, 12 and 14, 12 Zero 12, 72 and 12, 52 Undefined 4 514, 32 and 14, 42 Undefined b 5 6a b 1 2 42. 43. 44. a 2 5a b a 3 1 b and a2, 13, 12 and 15, 62 2 84 3 , 3b and a 1 2 3 4b 9 2 3 20 45. , 46. , 47. 16, 52 and 110, 42 1 11.4, 0.52 and 10.8, 1.32 3 10.25, 3.42 and 10.23, 2.22 4 48. 49. 50. 16.8, 3.42 and 13.2, 1.12 13.15, 8.252 and 16.85, 4.252 11994, 3.52 and 12000, 2.62 51. 52. 53. 54. 11988, 4.652 and 11998, 9.252 Concept 3: Parallel and Perpendicular Lines For Exercises 55–60, the slope of a line is given. (See Example 6.) a. Determine the slope of a line parallel to the given line. b. Determine the slope of a line perpendicular to the given line. 55. 56. m 2 3 m 2 57. m 0 58. The slope is undefined. 4 5 a. 0 b. Undefined a. Undefined b. 0 59. 60. m m 4 For Exercises 61–66, let and represent the slopes of two lines. Determine if the lines are parallel, perpendicular, or neither. (See Example 6.) 3 2 2 3 1 2 m1 m2 61. 62. 63. m2 m1 1, 2 7 m2 , 2 7 8 6 m1 2, 3 4 m1 64. 65. 66. m2 4 4 m2 m1 5, m2 5 m2 m1 , m1 , For Exercises 67–72, find the slopes of the lines l1 and l2 defined by the two given points. Then determine whether l1 and l2 are parallel, perpendicular, or neither. (See Example 7.) 67. 68. 69. l1: 12, 42 and 11, 22 l1: 10, 02 and 12, 42 l1: 11, 92 and 10, 42 l2: 11, 72 and 10, 52 l2: 11, 52 and 11, 12 l2: 15, 22 and 110, 12 1 5 l1: 13, 42 and 11, 82 l1: 14, 42 and 10, 32 l1: 13, 52 and 12, 52 70. 71. 72. l2: 15, 52 and 12, 22 l2: 11, 72 and 11, 12 l2: 12, 02 and 14, 32 60 0.45 or 9 20 0.46 or 23 50 1 4 Writing Translating Expression Geometry Scientific Calculator Video 2 7 , 1 3b and a8 7 , , 3 5b and a1 4 , 3 12, 42 and 11, 32 1 4 3 1 2 3 5 49 60 7 8 28 5 or 5 4 1.25 0.15 or 3 20 a. 2 b. 1 2 a. 4 b. 1 4 a. 2 3 b. 3 2 a. 4 5 b. 5 4 Perpendicular Neither Parallel Perpendicular Neither Parallel l1: m 2, l2: m 2; parallel l1: m 5, l2: m ; perpendicular l1: m 1, l2: m 1; perpendicular l ; neither 1: m 1 2 , l2: m 4 l1: m 2, l2: m ; neither l1: m 2, l2: m 2; parallel
miller_introductory_algebra_3e_ch1_3
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