Parallel and Perpendicular Lines ALGEBRA 1 LESSON 6-5 pages 314–317  Exercises 1. 2. – 3. 1 4. 0 5. – 6. 7 7. no, different slopes 8. yes, same slopes and different y-intercepts 9. yes, same slopes and 10. no, different slopes 11. yes, same slopes and 12. yes, same slopes and 13. y = 6x 14. y = –3x + 9 15. y = –2x – 1 16. y = – x – 20 17. y = 0.5x – 9 18. y = – x + 19. – 20. 21. – 22. 5 1 2 3 4 23. 24. undefined 25. y = – x 26. y = –x + 10 27. y = 3x – 10 28. y = x + 29. y = – x + 24 30. y = – x + 2 31. y = x + 1 32. perpendicular 33. parallel 34. perpendicular 7 5 11 6-5

Parallel and Perpendicular Lines ALGEBRA 1 LESSON 6-5 35. neither 36. parallel 37. perpendicular 38. parallel 39. neither 40. perpendicular 41. neither 42. Answers may vary. Sample: same x and y coefficients 43. y = – x – ; y = – x + 44. y = x + y = –3x + 7 45. y = – x y = 2x 46. y = x + ; y = x – 47. y = 4; y = 2 48. y = x; y = –x + 1 49. about 50. Answers may vary. Sample: same slope of – 51. Answers may vary. Sample: • – = –1 4 5 19 3 1 52. a. The screen is not square. b. The lines appear perpendicular. 53. Answers may vary. Sample: y = 4x + 1 54. No; the slopes are not equal. 55. No; the slopes are not neg. reciprocals. 56. yes; same slopes and different y-intercepts 57. False; the product of two positive numbers can’t be –1. 58. True; y = x + 2 and y = x + 3 are parallel. 2 21 / 6-5

Parallel and Perpendicular Lines ALGEBRA 1 LESSON 6-5 59. False; all direct variations go through the point (0, 0). If they have the same slope, they are the same line, not parallel lines. 60. The slopes of AD and BC are both undefined, so they are parallel. The slopes of AB and CD are both so they are parallel. The quadrilateral is a parallelogram. 2 5 61. The slope of JK is . The slope of KL is –2. The slope of LM is . The slope of JM is –4. The quadrilateral is not a parallelogram. 62. The slopes of PQ and RS are both – .The slopes of QR and SP are both – .The quadrilateral is 1 6 3 63. The slopes of AB and CD are both .The slopes of BC and AD are both – . The product is –1, so the quadrilateral is a rectangle. 64. The slopes of KL and MN are both – .The slopes of LM and KN are both 5. The product is not –1, so the quadrilateral is not a rectangle. 6-5

Parallel and Perpendicular Lines ALGEBRA 1 LESSON 6-5 The diagonal AC has a slope of . The diagonals are perpendicular. ABCD is a rhombus. 67. RP has a slope of . RQ has a slope of – . RP is the neg. reciprocal of RQ, so PQR is a right triangle. 68. parallel 69. perpendicular 65. The slopes of PQ and RS are both . The slopes of PS and QR are both –2. The product is –1, so the quadrilateral is a rectangle. 66. BC and AD both have a slope of zero. BC and AD are parallel. AB and CD both have a slope of . AB and CD are parallel. The diagonal BD has a slope of –2. 1 2 4 3 70. y = – x – ; y = x + 7 71. y = x – 3; y = –2x + 7 72. –1.5; 24 73. D 74. F 75. C 8 17 6-5

Parallel and Perpendicular Lines ALGEBRA 1 LESSON 6-5 76. [2] Find slope of 2x + y = 3: y = –2x + 3, therefore slope is –2. Find x: = –2, = –2, –4 = –2 + 2x, x = –1 (OR equivalent explanation) [1] correct value of x but no work OR minor computation error in work 77. C 78. A 79. B 80. y = 3x + 4 81. y = –4x – 8 82. y + 3 = (x – 5) 83. y + 9 = – (x + 1) 84. y – 4 = – (x + 6) 85. y – 11 = (x – 7) 86. 7; 11; 15 87. –9; –17; –25 88. yes 2 – 6 1 – x – 4 89. yes 90. no 91. yes 3 4 2 5 1 6-5