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miller_intermediate_algebra_4e_ch1_3

136 Chapter 2 Linear Equations in Two Variables and Functions Answer 9. a. x-intercept: (7.5, 0); y-intercept: (0, 30) b. The x-intercept (7.5, 0) represents the amount of fuel in the truck after 7.5 hr. After 7.5 hr the tank contains 0 gal. It is empty. c. The y-intercept (0, 30) represents the amount of fuel in the truck initially (after 0 hr). After 0 hr, the tank contains 30 gal of fuel. 70,000 60,000 50,000 40,000 30,000 20,000 10,000 y Taxable Value of a Truck Versus the Age of the Vehicle 0 0 1 2 3 4 5 6 x Taxable Value ($) Age (years) b. The x-intercept (5, 0) indicates that when the truck is 5 yr old, the taxable value of the truck will be $0. c. The y-intercept (0, 65,000) indicates that when the truck was new (0 yr old), its taxable value was $65,000. Skill Practice 9. Acme Motor Company tests the engines of its trucks by running the engines in a laboratory.The engines burn 4 gal of fuel per hour.The engines begin the test with 30 gal of fuel.The equation y 30 4x represents the amount of fuel y left in the engine after x hours. a. Find the x- and y-intercepts. b. Interpret the x-intercept in the context of this problem. c. Interpret the y-intercept in the context of this problem. TIP: In Example 7 we graphed the line only in the first quadrant where both the x- and y-coordinates are positive. (A negative x-coordinate would imply a negative age, and a negative y-coordinate would imply a negative value of a car, neither of which makes sense.) 5. Horizontal and Vertical Lines Recall that a linear equation can be written in the form where A and B are not both zero. If either A or B is 0, then the resulting line is horizontal or vertical, respectively. Vertical and Horizontal Lines 1. A vertical line is a line whose equation can be written in the form where k is a constant. 2. A horizontal line is a line whose equation can be written in the form y k, where k is a constant. x k, Ax By C, Graphing a Vertical Line x 6. Example 8 Graph the equation Solution: Because this equation is in the form the line is vertical and must cross the x-axis at .We can also construct a table of solutions to the equation x 6 x 6 x k, . The choice for the x-coordinate must be 6, but y can be any real number (Figure 2-10).


miller_intermediate_algebra_4e_ch1_3
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