228 Chapter 3 Graphing Linear Equations in Two Variables 30. 31. 32. 5 4 y 1 543 1 2 3 4 5 21 2 3 4 5 5 4 y 1 1 5 4 y 1 1 For Exercises 33–50, find the slope of the line that passes through the two points. (See Examples 2–5.) 33. 34. 35. 12, 42 and 14, 22 15, 42 and 111, 122 12, 32 and 11, 62 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 10, 12 and 14, 12 12, 72 and 12, 52 1 2 3 5 1 4 4 5 14, 32 and 14, 42 b a b and a b 42. 43. 44. a 2 7 , 1 3 b and a 8 7 , 5 6 , , 13, 12 and 15, 62 16, 52 and 110, 42 16.8, 3.42 and 13.2, 1.12 45. 46. 47. 13.15, 8.252 and 16.85, 4.252 11994, 3.52 and 12000, 2.62 11988, 4.652 and 11998, 9.252 48. 49. 50. Concept 3: Parallel and Perpendicular Lines For Exercises 51–56, the slope of a line is given. (See Example 6.) a. Determine the slope of a line parallel to the line with the given slope. b. Determine the slope of a line perpendicular to the line with the given slope. 2 3 51. 52. 53. m m 0 4 5 m 2 54. The slope is undefined. 55. 56. m m 4 For Exercises 57–62, 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 57. 58. 59. m2 m1 1, 2 7 m2 , 2 7 8 6 m1 2, 3 4 m1 60. 61. 62. m2 4 4 m2 m1 5, m2 5 m2 m1 , m1 , For Exercises 63–68, 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.) 63. 64. 65. 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 l1: 13, 42 and 11, 82 l1: 14, 42 and 10, 32 l1: 13, 52 and 12, 52 66. 67. 68. l2: 15, 52 and 12, 22 l2: 11, 72 and 11, 12 l2: 12, 02 and 14, 32 x 3 2 1 1 2 3 4 5 2 3 4 5 x 3 2 1 2 3 4 5 54 321 2 3 4 5 x 3 2 54 321
miller_beginning_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above