Algebraic For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular: 4x7y= 10 7x+4y=1 3y+x= 12 y= 8x+1 3y+4x= 12 -6y= 8x+1 6x-9y=10 3x+2y=1 6. 't'\" I50 1o.y=%x+1 3x+2y=1 -3 x+1 11 y 4 _' -3x + 4y = 1 For the following exercises, find the x- and yintercepts of each equation 12.f(x) = -x+ 2 a. g (x) = 2x + 4 14. h(x) = 3x- 5 E. k(x) = -5x+1 16. 2x+ 5y = 20 . 7x + 2y = 56 For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither? 18. . Line 1: Passes through (0, 6) and (3,-24) . Line 2: Passes through (-1, 19) and (8, -71) 19. . Line 1: Passes through (8, 55) and (10, 89) . Line 2: Passes through (9, -44) and (4, -14) _ ., For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither? 18. . Line 1: Passes through (0, 6) and (3,-24) . Line 2: Passes through (-1, 19) and (8, -71) . Line 1: Passes through (8, 55) and (10, 89) . Line 2: Passes through (9, -44) and (4, -14) 20. . Line 1: Passes through (2, 3) and (4,-1) . Line 2: Passes through (6, 3) and (8, 5) . Line 1: Passes through (1,7) and (5, 5) 0 Line 2: Passes through (-1, -3)and (1,1) 22. . Line 1: Passes through (0, 5) and (3, 3) . Line 2: Passes through (1,-5) and (3, -2) . Line 1: Passes through (2, 5) and (5,-1) . Line 2: Passes through (3, 7) and (3, -5) 24. Write an equation for a line parallel to f (x) = -5x - 3 and passing through the point (2, -12). 25. Write an equation for a line parallel to g(x) = 3x - 1 and passing through the point (4, 9). 26. Write an equation for a line perpendicular to h(t) = -2t + 4 and passing through the point (4, -1). 27. Write an equation for a line perpendicular to p(t) = 3: + 4 and passing through the point (3 , 1). 28. Find the point at which the line f(x) = -2x - 1 intersects the line g(x) = -x. 29. Find the point at which the line f(x) = 2x + 5 intersects the line g(x) = -3x - 5. 30. Use algebra to find the point at which the line f (x) = -%x + 22754 intersects the line _ 73 h (x) Tax + 115- a. Use algebra to find the point at which the line f (x) = %x + 1507 intersects the line g(x)= 15:): + 35}. For the following exercises, sketch the graph of each equation. 44. f (x) = -2x - 1 45. g (x) = -3x + 2 46. h (x) = 4x+ 2 47. k (x) = 3x - 3 48. f (t) = 3 + 2t 49. p (t) = -2 + 3t 50. x = 3 51. x = -2 52. r (x) = 4 53. q (x) = 3 54. 4x = -9y + 36 55. 3 - 4 = 1 56. 3x - 5y = 15 57. 3x = 15 58. 3y = 12 59. If g(x) is the transformation of f (x) = x after a vertical compression by >, a shift right by 2, and a shift down by 4 @ Write an equation for g (x). What is the slope of this line? Find the y-intercept of this line. 60. If g(x) is the transformation of f (x) = x after a vertical compression by 3, a shift left by 1, and a shift up by 3 @ Write an equation for g (x) . What is the slope of this line? Find the y-intercept of this line.For the following exercises,, write the equation of the line shown in the graph. 61. 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 62. HNWAG RK -6 -5 -4 -3 -2 -1 0 1 2 3 5 6 -3- 63. HNWAS OK + X -6 -4 -2 -1 0 1 2 3 4 5 6 -1- -2- -3- -4- -5- -6For the following exercises, find the point of intersection of each pair of lines if it exists. If it does not exist, indicate that there is no point of intersection. y = ix+ 1 65. -3x + 4y = 12 66. 2x - 3y = 12 5y + x = 30 67. 2x = y - 3 y + 4x = 15 * - 2y + 2 : 3 x- y = 3 5x + 3y = -65 69. x - y = -5 Extensions 70. Find the equation of the line parallel to the line g (x) = -0.01x + 2.01 through the point (1, 2). 71. Find the equation of the line perpendicular to the line g (x) = -0.01x+2.01 through the point (1, 2). For the following exercises, use the functions f (x) = -0.1x+200 and g (x) = 20x + 0.1. 72. Find the point of intersection of the lines f and g. 73. Where is f (x) greater than g (x)? Where is g (x) greater than f (x)? Real-World Applications 74. A car rental company offers two plans for renting a car. Plan A: $30 per day and $0.18 per mile Plan B: $50 per day with free unlimited mileage How many miles would you need to drive for plan B to save you money? 75. A cell phone company offers two plans for minutes. Plan A: $20 per month and $1 for every one hundred texts. Plan B: $50 per month with free unlimited texts. How many texts would you need to send per month for plan B to save you money? 76. A cell phone company offers two plans for minutes. Plan A: $15 per month and $2 for every 300 texts. Plan B: $25 per month and $0.50 for every 100 texts. How many texts would you need to send per month for plan B to save you money