342 CHAPTER 6 Algebra, Graphs, and Functions In Step 4 of the procedure, if the points are not in a straight line, recheck your calculations and determine your error. Graphing by Using the -x and y-Intercepts Example 3 contained two special points on the graph, ( 1, 0) − and (0, 2). At these points, the line crosses the x-axis and the y-axis, respectively. The ordered pairs ( 1, 0) − and (0, 2) represent the -x intercept and the -y intercept, respectively. Another method that can be used to graph linear equations is to determine the x- and y-intercepts of the graph. DETERMINING THE X- AND -INTERCEPTS Y To determine the x-intercept, set y 0 = and solve the equation for x. To determine the y-intercept, set x 0 = and solve the equation for y. PROCEDURE A linear equation may be graphed by determining the x- and y-intercepts, plotting the intercepts, and drawing a straight line through the intercepts. When graphing by this method, you should always plot a checkpoint before drawing your graph. To obtain a checkpoint, select a nonzero value for x and determine the corresponding value of y. The checkpoint should be collinear with the x- and y-intercepts. Example 4 Graphing an Equation by Using Intercepts Graph x y 2 3 6 + = by using the x- and y-intercepts. Solution To determine the x-intercept, set y 0 = and solve for x. x y x x x 2 3 6 2 3(0) 6 2 6 3 + = + = = = The x-intercept is (3, 0). To determine the y-intercept, set x 0 = and solve for y. + = + = = = x y y y y 2 3 6 2(0) 3 6 3 6 2 The y-intercept is (0, 2). As a checkpoint, substitute x 3 = − and determine the corresponding value for y. + = − + = − + = = = x y y y y y 2 3 6 2( 3) 3 6 6 3 6 3 12 4
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