Decision method for elementary algebra by Seidenberg A.

By Seidenberg A.

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L1: ͑0, Ϫ1͒, ͑5, 9͒ 66. L1: ͑Ϫ2, Ϫ1͒, ͑1, 5͒ L2: ͑0, 3͒, ͑4, 1͒ L2: ͑1, 3͒, ͑5, Ϫ5͒ 67. L1: ͑3, 6͒, ͑Ϫ6, 0͒ 68. L1: (4, 8), (Ϫ4, 2) L2: ͑0, Ϫ1͒, ͑5, 73 ͒ L2: ͑3, Ϫ5͒, ͑Ϫ1, 13 ͒ In Exercises 69–78, write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line. Point Line 69. ͑2, 1͒ 4x Ϫ 2y ϭ 3 70. ͑Ϫ3, 2͒ xϩyϭ7 71. 72. ͑ ͑ Ϫ 23, 78 7 3 8, 4 ͒ ͒ 3x ϩ 4y ϭ 7 5x ϩ 3y ϭ 0 73. ͑Ϫ1, 0͒ y ϭ Ϫ3 74. ͑4, Ϫ2͒ yϭ1 75.

42 Production cost Cost equation Describe the practical significance of the y-intercept and slope of this line. Marginal cost: m = $25 50 Using Slope as a Rate of Change 150 The y-intercept ͑0, 3500͒ tells you that the cost of producing zero units is $3500. This is the fixed cost of production—it includes costs that must be paid regardless of the number of units produced. 42. Economists call the cost per unit the marginal cost. If the production increases by one unit, then the “margin,” or extra amount of cost, is $25.

Y y (b , c) (a + b , c) (x0 , y0 ) x x (0, 0) (a) Sketch scatter plots of these two sets of data on the same set of coordinate axes. (b) Find the year in which the numbers of men’s and women’s teams were nearly equal. (c) Find the year in which the difference between the numbers of men’s and women’s teams was the greatest. What was this difference? 71. Make a Conjecture Plot the points ͑2, 1͒, ͑Ϫ3, 5͒, and ͑7, Ϫ3͒ on a rectangular coordinate system. Then change the sign of the x-coordinate of each point and plot the three new points on the same rectangular coordinate system.

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