Section 3.2 Graphing Linear Equations 219 Solution 5b. i. The x- and y-intercepts of y = -4000x + 32,000 are shown next. x y Meaning 0=-4000x + 32,000 4000x = 32,000 4000x 4000 = 32,000 4000 x = 8 0 The x-intercept is (8, 0). It means that when the truck is 8 yr old, its value is $0. 0 y = -4000(0) + 32,000 y = 32,000 The y-intercept is (0, 32,000). It means that when the truck is 0 yr old, or when it is new, its value is $32,000. ii. The value of the truck after 2 yr and after 4 yr is shown next. x y Meaning 2 y = -4000(2) + 32,000 y = -8000 + 32,000 y = 24,000 The point is (2, 24,000). It means that in 2 yr, the value of the truck is $24,000. 4 y = -4000(4) + 32,000 y = -16,000 + 32,000 y = 16,000 The point is (4, 16,000). It means that in 4 yr, the value of the truck is $16,000. iii. The graph of the equation is found by plotting the points (8, 0), (0, 32,000), (2, 24,000), and (4, 16,000). Because the y-values range from 0 to 32,000, we let each tick mark on the y-axis represent 4000 units. Also, the graph is drawn only in Quadrant I since it doesn’t make sense for the years to be negative or for the value of the truck to be negative. 0, 32,000 2, 24,000 4, 16,000 8, 0 36000 32000 28000 24000 20000 16000 12000 8000 4000 0 1 2 3 4 5 6 7 8 9 10 Student Check 5 The median annual income for women with a bachelor’s degree is given by the equation y = 1100x + 27,645, where x is the number of years after 1990. (Source: www .infoplease.com) a. Find the y-intercept of the equation and interpret its meaning in the context of this problem. b. Find the median annual income for the years 2000 and 2010. c. Use the information in parts (a) and (b) to graph the equation. Troubleshooting Common Errors Some common errors associated with graphing linear equations in two variables are illustrated next. Objective 6 ▶ Troubleshoot common errors.
hendricks_beginning_intermediate_algebra_1e_ch1_3
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