Section 1.5 AN3 13. (a) = Slope 1 2 (b) If x increases by 2 units, y will increase by 1 unit. 15. (a) = − Slope 1 3 (b) If x increases by 3 units, y will decrease by 1 unit. 17. = − Slope 3 2 y 8 x 8 (2, 3) (4, 0) 19. = − Slope 1 2 y 5 x 5 (2, 1) ( 2, 3) 25. y 8 x 5 (2, 5) 3 1 P (1, 2) 27. y 8 x 7 4 (6, 1) 3 P (2, 4) 29. y 5 x 5 P ( 1, 3) 31. y 5 x 5 P (0, 3) 33. ( ) − = − y x 2 3 1 35. ( ) − = − − y x 4 3 4 2 37. − = y 3 0 39. ( ) ( ) ( ) 2, 6 ; 3, 10 ; 4, 14 41. ( ) ( ) ( ) − − − 4, 7; 6, 10; 8, 13 43. ( ) ( ) ( ) − − − − 1, 5; 0, 7; 1, 9 45. − = = x y y x 2 0 or 1 2 47. + = = − + x y y x 2 or 2 49. − = = − x y y x 2 3 or 2 3 51. + = = − + x y y x 2 5 or 1 2 5 2 53. − = − = + x y y x 3 9 or 3 9 55. − = = − x y y x 2 1 or 1 2 1 2 57. − = − = + x y y x 2 5 or 1 2 5 2 59. + = = − + x y y x 3 3 or 3 3 61. − = − = + x y y x 4 or 4 63. = x 2; no slope-intercept form 65. = y 2 67. − = − = + x y y x 2 4 or 2 4 69. − = = x y y x 2 0 or 1 2 71. = x 4; no slope-intercept form 73. + = = − x y y x 2 0 or 2 75. + = = − + x y y x 2 4 or 2 4 77. = y 4 79. = = y Slope 2; -intercept 3 y 8 x 5 (1, 5) (0, 3) 81. = = − y Slope 2; -intercept 2 y 5 x 5 (1, 0) (0, 2) 87. = = − y Slope 2 3 ; -intercept 2 y 5 x 5 (3, 0) (0, 2) 103. (a) x-intercept: 3; y-intercept: 21 2 (b) y 12 x 5 (3, 0) 21 2 0, 105. (a) x-intercept: 2; y-intercept: 3 (b) y 5 x 5 (0, 3) (2, 0) 107. (a) x-intercept: 5; y-intercept: −2 (b) y 5 x 6 (5, 0) (0, 2) 109. = y 0 111. Parallel 113. Neither 115. − = − = + x y y x 2 or 2 117. + = = − + x y y x 3 3 or 1 3 1 119. ( ) ( ) ( ) ( ) = − = = − = = − = P P m P P m 2, 5 , 1, 3 , 2 3 ; 1, 3 , 1, 0 , 3 2 ; 1 2 1 2 3 2 because = − mm 1 1 2 , the lines are perpendicular and the points ( ) ( ) ( ) − − 2, 5 , 1, 3 , and 1, 0 are the vertices of a right triangle. 121. P P m P P m P P m P P m 1, 0 , 2, 3 , 1; 1, 2, 4, 1 , 1; 1, 0 , 1, 2, 1; 2, 3 , 4, 1 , 1; 1 2 3 4 1 3 2 4 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = − = = = − = = = − = − =− = = =− opposite sides are parallel, and adjacent sides are perpendicular; the points are the vertices of a rectangle. 123. = + C x 0.60 39; $105.00; $177.00 125. = + C x 0.28 6578 21. = Slope 0 y 5 x 5 (2, 1) (3, 1) 23. Slope undefined y 5 x 5 ( 1, 2) (1, 2) 83. = = y Slope 1 2 ; -intercept 2 y 5 x 5 (0, 2) (2, 3) 85. = − = y Slope 1 2 ; -intercept 2 y 5 x 5 (0, 2) (4, 0) 89. = − = y Slope 1; -intercept 1 y 2.5 x 2.5 (0, 1) (1, 0) 91. Slope undefined; no y-intercept y 5 x 5 ( 4, 0) 93. = = y Slope 0; -intercept 5 y 8 x 5 (0, 5) 95. = = y Slope 1; -intercept 0 y 5 x 5 (0, 0) (1, 1) (2, 2) 97. = = y Slope 3 2 ; -intercept 0 5 x 5 (0, 0) (2, 3) y 99. (a) x-intercept: 3; y-intercept: 2 (b) y 5 x 5 (0, 2) (3, 0) 101. (a) x-intercept: −10; y-intercept: 8 (b) y 10 x 8 ( 10, 0) (0, 8) 127. (a) = + C x 17 0.13 (b) y x (0, 17) (150, 36.5) 20 40 0 50 100 150 (c) $23.50 (d) $32.60 (e) For every 1-mile increase in distance traveled, the cost will increase 13 cents. 129. ( ) ° = ° − C 5 9 F 32 ; approximately ° 21.1 C 131. (a) = − + y x 2 25 30 (b) x-intercept: 375; The ramp meets the floor 375 in. (31.25 ft) from the base of the platform. (c) The ramp does not meet design requirements. It has a run of 31.25 ft. (d) The only slope possible for the ramp to comply with the requirement is for it to drop 1 in. for every 12-in. run. 133. (a) = + A x 1 5 20,000 (b) $80,000 (c) Each additional box sold requires an additional $0.20 in advertising. 135. − − 2, 2 3 , 1 2 137. ( ) +a b c 3 , 3 139. b, c, e, g 141. c 147. No; no 149. They are the same line. 151. Yes, if the y-intercept is 0.
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