Section 3.2 Graphing Linear Equations 213 Plotting these points and connecting them gives us the graph of x - 2y = 4. (0, –2) (–2, –3) 2 –4 –2 2 4 –4 –6 x y 32 1, – Student Check 2 Graph each equation. a. y = x - 2 b. y=- 1 3 x + 6 c. x + 3y = 9 Finding Intercepts Another method of graphing a linear equation in two variables involves finding two important points that lie on the graph of the line. These points are called the intercepts of the graph. ������������������������ The x-intercept is the point on the graph where the graph intersects the x-axis. The y-intercept is the point on the graph where the graph intersects the y-axis. In the graph from Example 2b, the x-intercept is (3, 0) and the y-intercept is (0, -4). Notice the x-intercept has a y-coordinate of zero since every point on the x-axis has a y-coordinate of zero. Similarly, the y-intercept has an x-coordinate of zero since every point on the y-axis has an x-coordinate of zero. x-intercept y-intercept 2 (3, 0) (0, –4) (–3, –8) –2 –4 –2 –6 –8 x y ���������������������� Finding the Intercepts Step 1: To find the x-intercept, replace y with 0 and solve for x. The point will always be of the form (a, 0). Step 2: To find the y-intercept, replace x with 0 and solve for y. The point will always be of the form (0, b). ������������ While we can graph a line knowing only two points, it can be helpful to find a third point as a checkpoint. Objective 3 ▶ Use intercepts to graph linear equations in two variables.
hendricks_beginning_algebra_1e_ch1_3
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