Chapter 2 Review Exercises
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54. 9x – 4y = 2. Solve for y to put the equation in slopeintercept form. 4 y 9x 2 y 9 x 1 4 2
(continued)
Thus, the slope is 49 . 55. x 2 0 x 2 The graph is a vertical line, through (2, 0). The slope is undefined. 48. Line through (2, – 4), m 3 4 First locate the point (2, – 4). Because the slope is 43 , a change of 4 units horizontally (4 units to the right) produces a change of 3 units vertically (3 units up). This gives a second point, (6, –1), which can be used to complete the graph.
50. through (8, 7) and m
, 2
2
y2 y1 2 7 9 1 8 2x x1 2 2 18 6 9 15 15
m
0 30
15
(c) The number of jobs lost in December is approximately 6000. The number of jobs gained in January is approximately 2000.
5
(d) It shows a slight downward trend.
52. through (5, 6) and (5, –2) y y 26 8 m 2 1 x2 x1 55 0 The slope is undefined. 53. 11x 2 y 3 Solve for y to put the equation in slopeintercept form. 3 2 y 11x 3 y 2 x 2 11 11
57. Initially, the car is at home. After traveling for 30 mph for 1 hr, the car is 30 mi away from home. During the second hour the car travels 20 mph until it is 50 mi away. During the third hour the car travels toward home at 30 mph until it is 20 mi away. During the fourth hour the car travels away from home at 40 mph until it is 60 mi away from home. During the last hour, the car travels 60 mi at 60 mph until it arrived home.
2
0 3
Thus, the slope is
1 5.
(b) The lowest point on the graph occurs in December, so the most jobs lost occurred in December. The highest point on the graph occurs in January, so the most jobs gained occurred in January.
51. through (0, –7) and (3, –7) 77
Thus, the slope is
58. (a) This is the graph of a function because no vertical line intersects the graph in more than one point.
49. through (2, –2) and (3, – 4) y y 42 2 m 2 1 2 32 1 x2 x1 1
56. x – 5y = 0. Solve for y to put the equation in slopeintercept form. 5y x y 1 x 5
.
2
59. (a) We need to first find the slope of a line that passes between points (0, 30.7) and (12, 82.9) y y 82.9 30.7 52.2 m 2 1 4.35 x2 x1 12 0 12 Now use the point-intercept form with b = 30.7 and m = 4.35. y = 4.35x + 30.7 The slope, 4.35, indicates that the number of e-filing taxpayers increased by 4.35% each year from 2001 to 2013. (b) For 2009, we evaluate the function for x = 8. y = 4.35(8) + 30.7 = 65.5 65.5% of the tax returns are predicted to have been filed electronically.
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