6.6 Graphing Linear Equations 349 47. y x3 6 + = * 48. y x4 8 − = * 49. y x 4 1 2 = + * 50. y x 3 2 3 = − * 51. y x 1 3 = * 52. y x 2 3 = − * In Exercises 53– 62, graph the equation, using the x- and y intercepts - , as in Example 4. 53. x y 2 + = * 54. x y 4 − = * 55. x y 1 + = * 56. x y 3 − = * 57. x y 2 6 + = * 58. x y 3 6 − = − * 59. x y2 6 + = * 60. x y 2 4 − = * 61. x y 2 4 8 = − − * 62. x y 6 3 9 = − * In Exercises 63–70, determine the slope of the line through the given points. If the slope is undefined, so state. 63. (3, 5) and (5, 9) 2 64. (4, 3) and (3, 4) 1− 65. (5, 1) and (8, 8) 7 3 66. ( 2, 6) − and ( 4, 9) − 3 2 − 67. (1, 5) and (4, 5) 0 68. ( 3, 4) − − and (5, 4) − 0 69. (8, 3) − and (8, 3) Undefined 70. (2, 6) and (2, 3) − Undefined In Exercises 71–78, graph the equation using the slope and y-intercept, as in Examples 6 and 7. 71. y x 2 = + * 72. y x 2 = − − * 73. y x2 3 = − + * 74. y x3 1 = − * 75. y x 1 1 2 = − + * 76. y x 2 1 2 = − * 77. x y 3 2 6 0 − + = * 78. x y 3 4 8 0 + − = * In Exercises 79–82, determine the equation of the graph. 79. y x 4 5 2 1 21 1 2 3 4 21 22 3 5 y x 3 4 3 = − + 80. y x 3 21 2221 1 2 3 4 23 1 2 y x 2 3 2 = + In Exercises 83–86, graph the equation and state the slope of the line if the slope exists (see Example 9). 83. x 3 = * 84. x 2 = − * 85. y 3 = * 86. y 4 = − * In Exercises 87–90, determine the equation of the graph. 87. y 4 5 25 3 1 2 21 23 24 2221 2423 25 1 2 3 4 x 5 22 y 2 = − 88. y 4 5 25 3 1 2 21 22 23 24 2221 2423 25 1 2 3 x 4 5 x 4 = 89. y 4 5 25 3 1 2 21 22 23 24 2221 24 25 1 2 3 4 x 23 5 x 3 = − 90. y 4 5 25 3 2 21 22 23 24 2221 2423 25 1 2 3 4 x 1 5 y 1 = Problem Solving In Exercises 91 and 92, points A B, , and C are three vertices of a rectangle. Plot the three points. (a) Determine the coordinates of the fourth point, D, to complete the rectangle. (b) Determine the area of the rectangle; use A lw. = 91. A B C ( 1, 4), (4, 4), ( 1, 2) − − a) D(4, 2) b) A 10 = square units 92. A B C ( 4, 2), (7, 2), (7, 8) − a) D( 4, 8) − b) A 66 = square units In Exercises 93 and 94, points A B, , and C are three vertices of a parallelogram (see Example 2) with sides parallel to the x axis - . Plot the three points. Determine the coordinates of the fourth point, D, to complete the parallelogram. Note: There are two possible answers for point D. 93. A(3, 2), B(5, 5), C(9, 5) (7, 2) or ( 1, 2) − 94. − − A B C ( 2, 2), (3, 2), (6, 1) (1, 1) − or (11, 1) − In Exercises 95–98, for what value of b will the line joining the points P and Q be parallel to the indicated axis? 95. P Q b x (2, 3), (6, ); -axis − 3− 96. P Q b y (4, 7), (,2); -axis − 4 97. P b Q y (3 1, 5), (8, 4); -axis − 3 98. P b Q x ( 6, 2 3), (7,1); -axis − + − 2− 81. 3 4 –2 y x 5 1 2 3 5 4 2 21 1 21 y x3 2 = + 82. y x 4 3 1 21 2 3 4 21 22 23 22 23 2 1 y x2 1 = − + *See Instructor Answer Appendix
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