236 Chapter 3 Graphing Linear Equations in Two Variables 75. Explain why not every line has both an x- and a y-intercept. A vertical line may not have a y-intercept. 76. Which of the lines has an x-intercept? A horizontal line may not have an x-intercept. 2x 3y 6 x 5 2y 8 x y 0 a, b, d 77. Which of the lines has a y-intercept? 78. a. b. c. d. a. y 2 b. x y 0 c. 2x 10 2 d. x 4y 8 a, b, d The store “CDs R US” sells all compact disks for $13.99. The following equation represents the revenue, y, (in dollars) generated by selling x CDs. y 13.99x 1x 02 a. Find y when x 13. y 181.87 b. Find xwhen . x 20 c. Write the ordered pairs from parts (a) and (b), and interpret their meaning in the context of the problem. d. Graph the ordered pairs and the line defined by the points. y 300 50 (20, 279.80) 79. The value of a car depreciates once it is driven off of the dealer’s lot. For a Hyundai Accent, the value of the car is given by the equation y where y is the value of the car in dollars x years after its purchase. (Source: Kelly Blue Book) a. Find y when b. Find x when . c. Write the ordered pairs from parts (a) and (b), and interpret their meaning in the context of the problem. x 1. y 7006 1531x 11,599 1x 02 y 279.80 x 3 (1, 10068) One year after purchase the value of the car is $10,068. (3, 7006) Three years after purchase the value of the car is $7006. y 10,068 250 200 0 2 4 6 8 10 12 14 16 18 20 Revenue ($) Number of Compact Disks 150 100 0 x (13, 181.87) (13, 181.87) Selling 13 compact disks yields $181.87 in revenue. (20, 279.80) Selling 20 compact disks yields $279.80 in revenue. Section 3.3 Slope of a Line and Rate of Change 1. Introduction to Slope The x- and y-intercepts represent the points where a line crosses the x- and y-axes. Another important feature of a line is its slope. Geometrically, the slope of a line measures the “steepness” of the line. For example, two hiking trails are depicted by the lines in Figure 3-14. Park Trail Mt. Dora Trail Figure 3-14 Expanding Your Skills Writing Translating Expression Geometry Scientific Calculator Video Concepts 1. Introduction to Slope 2. Slope Formula 3. Parallel and Perpendicular Lines 4. Applications of Slope: Rate of Change
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