134 Chapter 2 Linear Equations in Two Variables and Functions Finding the x- and y-Intercepts of a Line Example 5 Given 2x 4y 8 ,find the x- and y-intercepts. Then graph the equation. Solution: To find the x-intercept, substitute To find the y-intercept, substitute y 0. x 0 . 2x 4y 8 2x 4y 8 2102 2x 4102 4y 8 8 2x 8 4y 8 x 4 y 2 The x-intercept is (4, 0). The y-intercept is (0, 2). In this case, the intercepts are two distinct points and may be used to graph the line.A third point can be found to verify that the points all fall on the same line (points that lie on the same line are said to be collinear). Choose a different value for either x or y, such as . 2x 4y 8 y 4 2x 4142 y 4 8 Substitute . Solve for x. The point (4, 4) lines up with the other two points (Figure 2-8). 2x 16 8 2x 8 x 4 Skill Practice 7. Given 2x y 4, find the x- and y-intercepts.Then graph the equation. 5 4 3 2 1 543 1 2 3 4 5 Answer 7. 21 1 Figure 2-8 5 4 3 2 1 543 1 2 3 4 5 21 1 2 3 4 5 x y 2x + y 4 (2, 0) (0, 4) 2 3 4 5 x y (4, 0) (0, 2) (4, 4) 2x 4y 8 Finding the x- and y-Intercepts of a Line Example 6 y 14 Given find the x- and y-intercepts. Then graph the equation. Solution: To find the x-intercept, substitute To find the y-intercept, substitute . x, y 0. x 0 1 4 4y y x 1 x 102 1 1 x y 102 4 4 0 x y 0 The x-intercept is (0, 0). The y-intercept is (0, 0).
miller_intermediate_algebra_4e_ch1_3
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