240 Chapter 3 Linear Equations in Two Variables 1b. A truck’s value is given by y = -4000x + 32,000, where x is the age of the truck in years. 1c. The life expectancy for men in the United States can be approximated by y = 0.2x + 66, where x is the years after 1960. (Source: http://www.cdc.gov/nchs/ data/nvsr/nvsr56/nvsr56_09.pdf ) Solutions 1a. The x-value represents years worked and y represents salary in dollars. In y = 3500x + 45,000, the slope is m = 3500 = 3500 1 = change in salary change in years and the y-intercept is (0, 45,000). So, Jose’s initial salary is $45,000 and his salary increases by $3500 per year. From this information, we can obtain the following table of solutions. x y 0 45,000 0 + 1 = 1 45,000 + 3500 = 48,500 1 + 1 = 2 48,500 + 3500 = 52,000 1b. The x-value represents the age of the truck in years and y represents the value of the truck. In y = -4000x + 32,000, the slope is m=-4000 = - 4000 1 = change in value change in years and the y-intercept is (0, 32,000). So, the initial value of the truck is $32,000 and its value decreases by $4000 per year. From this information, we can obtain the following table of solutions. x y 0 32,000 0 + 1 = 1 32,000 - 4000 = 28,000 1 + 1 = 2 28,000 - 4000 = 24,000 1c. The x-value represents the years after 1960 and y represents life expectancy in years. In y = 0.2x + 66, the slope is m = 0.2 = 2 10 = 1 5 = change in life expectancy change in years after 1960 and the y-intercept is (0, 66). So, the life expectancy in 1960 was 66. Life expectancy increases 1 yr for every 5 yr after 1960. We can also say that life expectancy increases by 0.2 yr (2.4 months) for every year after 1960. From this information, we can obtain the following table of solutions. x y 0 66 0 + 5 = 5 66 + 1 = 67 5 + 5 = 10 67 + 1 = 68 Student Check 1 Interpret the slope and y-intercept in the context of each situation. Use the slope and y-intercept to create a table of three ordered pairs that satisfy the given equation. a. 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. b. A car’s value is given by y = -2500x + 15,000, where x is the age of the car. c. The daily cost to rent a car is y = 0.50x + 40, where x is the number of miles driven.
hendricks_beginning_algebra_1e_ch1_3
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