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218 Chapter 3 Linear Equations in Two Variables Solution 5a. i. The equation y = 1443x + 38,843 is a linear equation in two variables since each variable has a power of 1. ii. The y-intercept of y = 1443x + 38,843 is found by replacing x with 0 and solving for y. y = 1443x + 38,843 y = 1443(0) + 38,843 Substitute 0 for x. y = 0 + 38,843 Multiply. y = 38,843 Add. The y-intercept is the ordered pair (0, 38,843). This means that in 0 yr after 1990, or 1990, the median annual income for men with a bachelor’s degree was $38,843. iii. The x-intercept of y = 1443x + 38,843 is found by replacing y with 0 and solving for x. y = 1443x + 38,843 0 = 1443x + 38,843 Substitute 0 for y. 0 - 38,843 = 1443x + 38,843 - 38,843 Subtract 38,843 from each side. -38,843 = 1443x Simplify. -38,843 1443 = 1443x 1443 Divide each side by 1443. -26.9 ≈ x Simplify. The x-intercept is the ordered pair (-26.9, 0). This point does not make sense in the context of the problem since we cannot have a negative value for x. iv. The median annual income for 2000 is found by replacing x with 10 (2000 - 1990 = 10) and the income for 2010 is found by replacing x with 20 (2010 - 1990 = 20). Let x = 10: Let x = 20: y = 1443(10) + 38,843 y = 1443(20) + 38,843 y = 14,430 + 38,843 y = 28,860 + 38,843 y = 53,273 y = 67,703 In 2000, the median annual income was In 2010, the median annual income was $53,273. $67,703. 5b. Straight-line depreciation is the most common method of depreciating business assets. Mr. Rowell’s surveying company purchased a truck for their business. On the company’s tax records, Mr. Rowell must report the depreciated value of the truck. The truck’s value is given by y = -4000x + 32,000, where x is the age of the truck in years. i. Find the x- and y-intercepts and interpret their meaning in the context of this problem. ii. Find the value of the truck after 2 yr and after 4 yr. iii. Use the ordered pairs found in parts (i) and (ii) to draw the graph of the equation.


hendricks_beginning_algebra_1e_ch1_3
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