226 Chapter 3 Graphing Linear Equations in Two Variables Finding the x- and y-Intercepts of a Line Given the equation 3x 2y 8, a. Find the x-intercept. b. Find the y-intercept. c. Graph the equation. Solution: a. To find the x-intercept, b. To find the y-intercept, substitute substitute y 0. x 0. 3x 2y 8 3x 2y 8 3x 2102 8 3102 2y 8 3x 8 2y 8 3x 3 The x-intercept is c. The line through the ordered pairs and (0, 4) is shown in Figure 3-9. Note that the point 1 , 02 23 can be written as 12, 02. 83 The line represents the set of all solutions to the equation 3x 2y 8. 183 , 02 183 , 02. x 8 3 y 4 8 3 Example 5 5 4 3 2 1 21 Finding the x- and y-Intercepts of a Line Example 6 Given the equation 4x 5y 0 , a. Find the x-intercept. b. Find the y-intercept. c. Graph the equation. Solution: a. To find the x-intercept, b. To find the y-intercept, substitute substitute y 0. x 0. 4x 5y 0 4x 5y 0 4x 5102 0 4102 5y 0 4x 0 5y 0 x 0 y 0 The x-intercept is (0, 0). The y-intercept is (0, 0). Skill Practice Given the equation x 3y 4, 7. Find the x-intercept. 8. Find the y-intercept. 9. Graph the equation. Answers 7. (4, 0) 8. 9. 5 4 3 2 1 y 54 3 2 1 1 2 3 4 5 1 2 3 4 5 x a0, 4 3b The y-intercept is (0, 4). Figure 3-9 54 3 1 2 3 4 5 (0, 4) y x (2 , 0) 23 1 2 3 4 5 Classroom Example: p. 234, Exercise 50 83 Avoiding Mistakes Be sure to write the x- and y-intercepts as two separate ordered pairs: 1 , 02 and 10, 42.
miller_introductory_algebra_3e_ch1_3
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