Section 2.1 Linear Equations in Two Variables 143 45. A salesperson makes a base salary of $15,000 a year plus an 8% commission on total sales for the year.The yearly salary can be expressed as a linear equation. (See Example 7.) y 15,000 0.08x a. What is the salesperson’s salary for a year in which his sales total $500,000? b. What is the salary for a year in which sales total $300,000? c. What does the y-intercept mean in the context of this problem? d. Why is it unreasonable to use negative values for x in this equation? 20,000 0 0 Yearly Salary Versus Sales y 15,000 0.08x 200,000 40,000 400,000 60,000 600,000 80,000 800,000 100,000 Yearly Salary ($) Total Yearly Sales ($) x y 46. A taxi company in Portland charges $3.50 for any distance up to the first mile and $2.50 for every mile thereafter. The cost of a cab ride can be modeled graphically. a. Explain why the first part of the model is represented by a horizontal line. b. What does the y-intercept mean in the context of this problem? c. Explain why the line representing the cost of traveling more than 1 mi is not horizontal. d. How much would it cost to take a cab 3.5 mi? 35 30 25 20 15 10 5 Cost of Cab Ride Versus Number of Miles 1 2 4 5 7 8 10 11 47. A business owner buys several new computers for the office for $1500 each.The accounting office depreciates each computer by $300 per year.The value y (in $) for each computer can be represented by y 1500 300x, where x is the number of years after purchase. a. How much will a computer be worth 1 yr after purchase? b. After how many years will the computer be worth only $300? c. Determine the y-intercept and interpret its meaning in the context of this problem. d. Determine the x-intercept and interpret its meaning in the context of this problem. 300 Computer Value Versus Years After Purchase y 5 1500 2 300x 48. The equation y3.6x 59 can be used to approximate the air temperature y (in °F) at an altitude x (in 1000 ft). a. Determine the air temperature at 10,000 ft. b. At what altitude is the air temperature 5.8°F? c. Determine the y-intercept and interpret its meaning in the context of this problem. d. Determine the x-intercept and interpret its meaning in the context of this problem. 0 0 3 6 9 12 Cost ($) Number of Miles 3.50 x y 0 0 1 600 2 900 3 1200 4 5 1500 Value ($) Years After Purchase x y 60 40 20 0 220 Temperature (8F) Temperature Versus Altitude y 5 23.6 x 1 59 Altitude (1000 ft) x y 5 10 15 20
miller_intermediate_algebra_4e_ch1_3
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