Прямая на плоскости

1. y = x + 3, y = – x + 3; 2.y = x – 3, y = – x – 3; 3. y = – 1,5x; 5. 1) k = 2 / 3, b = – 2; 2) k = – 2 / 3, b = 0; 3) k = 0, b = – 3; 4) k = – 3 / 4, b = 3; 7. k = 1, b = 1, y = x + 1; 8. 1) x / 3 + y / (–2) = 1; 2) x / (– 4 / 3) + y / 2 = 1; 9. y = 0, 4x – 3y = 0, y = 4, 4x – 3y + 12 = 0; 10. x / 2 – y / 3 = 1 или – x / 4 + 2y / 3 = 1; 11. пр_ox = 8, пр_oy = 6, = 10; 12. A и C на прямой, В – выше, а D – ниже прямой; 15. AB = 4 , пр_ox = 4, пр_oy = 8; 16. Точки M₁, M₃ и M₄ лежат на данной прямой, точки M₂, M₅ и M₆ не лежат на ней; 17. (6, 0), (0, –4); 18. (3, –5); 19. A(2, –1), B(–1, 3), C(2, 4); 20. (1, –3), (–2, 5), (5, –9), (8, –17); 21. 1) k = 5, b = 3; 2) k = – 2 / 3, b = 2; 3) k = – 5 / 3, b = – 2 / 3; 4) k = – 3 / 2, b = 0; 5) k = 0, b = 3; 22. 1) – 5 / 3, 2) 3 / 5; 23. 1) 2x + 3y – 7 = 0, 2) 3x – 2y – 4 = 0; 24. 3x + 2y = 0, 2x – 3y – 13 = 0; 25. (2, 1), (4, 2), (–1, 7), (1, 8); 26. (–2, –1); 27. Q(11, –11); 28. 1) 3x – 2y – 7 = 0, 2) 5x + 7y – 7 = 0, 3) 8x + 12y + 5 = 0, 4) 5x + 7y + 9 = 0, 5) 6x – 30y – 7 = 0; 29. 5x – 2y – 33 = 0, x + 4y – 11 = 0, 7x + 6y + 33 = 0; 30. 7x – 2y – 12 = 0, 5x + y – 28 = 0, 2x – 3y – 18 = 0; 31. 4x + 3y – 11 = 0, x + y + 2 = 0, 3x + 2y – 13 = 0; 32. (3, 4); 33. 4x + y – 3 = 0; 34. Уравнение стороны АВ : 2x + y – 8 = 0, BC : x + 2y – 1 = 0, CA : x – y – 1 = 0. Уравнение медианы, проведенной из вершины А : x – 3 = 0, из вершины В : x + y – 3 = 0, из вершины С : y = 0. 35. 2x – 5y + 3 = 0, 2x – 5y – 26 = 0, 7x – 3y – 33 = 0; 36. 5x + y – 3 = 0, x – 5y – 11 = 0; 37. x + y – 8 = 0, 11x – y – 28 = 0; 38. (– 12, 5); 39. M₁(10, – 5); 40. x – 5y + 3 = 0 или 5x + y – 11 = 0; 41. 4x + 3y + 1 = 0, 3x – 4y + 32 = 0, 4x + 3y – 24 = 0, 3x – 4y + 7 = 0, x + 7y – 31 = 0; 42. Перпендикулярны 1), 3) и 4); 43. 1) j = 45°, j = 60°, j = 90°; 44. 3x + 7y – 5 = 0, 3x + 2y – 10 = 0, 9x + 11y + 5 = 0; 45. 1) (5, 6), 2) (3, 2), 3) (1 / 4, 1 / 3), 4) (2, – 1 / 11), 5) ( – 5 / 3, 2); 48. 1) при a ¹ 3; 2) при a = 3, b ¹ 2; 3) при a = 3, b = 2; 49. a = – 7; 50. 1) x / 3 + y / 2 = 1, 2) x / (– 6) + y / 8 = 1, 3) x / (9 / 2) + y / 3 = 1, 4) x / (2 / 3) + y / (– 2 / 5) = 1, 5) x / (1 / 5) + y / (1 / 2) = 1; 51. 6 кв.ед.; 52. ( + 1)x + ( – 1)y – 10 = 0, ( – 1)x + ( + 1)y + 10 = 0, x – y – 10 = 0; 53. 3x – 2y – 12 = 0, 3x – 8y + 24 = 0, 3x – 8y + 24 = 0; 54. (2, 0), (0, – 3) и (– 4, 0), (0, 3 / 2); 55. 1), 4), 6) и 8) заданы нормальными уравнениями; 56. 1) 4x / 5 – 3y / 5 – 2 = 0, 2) – 4x / 5 + 3y / 5 – 10 = 0, 3) –12x / 13 + 5y / 13– 1 = 0, 4) – x – 2 = 0, 5) 2x / – y / – 1 = 0; 57. 1) a= 0, p = 2; 2) a = p, p = 2; 3) a = p / 2, p = 3; 4) a= –p / 2, p = 3; 5) a = p / 6, p = 3; 6) a = p / 4, p = ; 7) a = – 2p / 3, p = 1; 8) a = – b, p = q; 9) a = b–p, p = q; 58. 1) d = – 3, d = 3; 2)d = 1, d = 1; 3)d = – 4, d = 4; 4) d = 0, d = 0 – точка Q лежит на прямой; 59. 1) по одну сторону; 2) по разные стороны; 3) по одну сторону; 4) по одну сторону; 5) по разные стороны; 60. 5 кв.ед.; 61. 6 кв.ед.; 64. 4; 65. 1) d = 2,5; 2) d = 3; 3) d = 0,5; 4) d = 3,5; 67. 3x + 4y + 6 = 0, 3x + 4y – 14 = 0 или 3x + 4y + 6 = 0, 3x + 4y + 26 = 0; 68. 12x – 5y + 61 = 0, 12x – 5y + 22 = 0 или 12x – 5y + 61 = 0, 12x – 5y + 100 = 0; 69. 4x + y + 5 = 0, y – 3 = 0; 70. 1) 3x + 2y – 7 = 0; 2) 2x – y = 0; 3) y – 2 = 0; 4) x – 1 = 0; 5) 4x + 3y – 10 = 0; 6) 3x – 2y + 1 = 0; 71.74x + 13y + 39 = 0; 72. x – y – 7 = 0; 73. 4x – 5y + 22 = 0; 4x + y – 18 = 0; 2x – y + 1 = 0; 74. x – 5y + 13 = 0; 5x + y + 13 = 0.