Section 3.2 Linear Equations in Two Variables 225 Answer 6. 5 4 3 2 1 y 5 43 21 1 2 3 4 5 1 2 3 4 5 x Let x 3: Let x 0: Let x 3: y 1 3 y 102 1 y 1 1 y 0 1 y 1 1 The line through the three ordered pairs 13, 02, 10, 12, 13, 22 and is shown in Figure 3-8. The 13 line represents the set of all solutions to the equation y x 1. y 0 y 1 y 2 1 3 y 132 1 1 3 132 1 y 1 3 x 1 5 4 3 543 2 1 1 2 3 4 5 1 2 3 4 5 (3, 2) (3, 0) (0, 1) y x 2 1 Figure 3-8 3. x- and y-Intercepts The x- and y-intercepts are the points where the graph intersects the x- and y-axes, respectively. From Example 4, we see that the x-intercept is at the point (3, 0) and the y-intercept is at the point (0, 1). See Figure 3-8. Notice that a y-intercept is a point on the y-axis and must have an x-coordinate of 0. Likewise, an x-intercept is a point on the x-axis and must have a y-coordinate of 0. In some applications, an x-intercept is defined as the x-coordinate of a point of intersection that a graph makes with the x-axis. For example, if an x-intercept is at the point (3, 0), it is sometimes stated simply as 3 (the y-coordinate is assumed to be 0). Similarly, a y-intercept is sometimes defined as the y-coordinate of a point of intersection that a graph makes with the y-axis. For example, if a y-intercept is at the point (0, 7), it may be stated simply as 7 (the x-coordinate is assumed to be 0). Although any two points may be used to graph a line, in some cases it is convenient to use the x- and y-intercepts of the line. To find the x- and y-intercepts of any two-variable equation in x and y, follow these steps: Classroom Example: p. 233, Exercise 38 Definitions of x- and y-Intercepts An x-intercept of a graph is a point 1a, 02 where the graph intersects the x-axis. A y-intercept of a graph is a point (0, b) where the graph intersects the y-axis. Finding x- and y-Intercepts Step 1 Find the x-intercept(s) by substituting into the equation and solving for x. y 0 Step 2 Find the y-intercept(s) by substituting into the equation and solving for y. x 0 x y 3 (3, ) 0 (0, ) 3 (3, ) x y 3 0 (3, 0) 0 1 (0, 1) 3 2 (3, 2) 12 Skill Practice Graph the equation. 6. y x 3
miller_introductory_algebra_3e_ch1_3
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