1. Copyright © 2013 Pearson Education, Inc. Section 3.3 More Graphing of Lines

2. Finding Intercepts The y-intercept is where the graph intersects the y-axis. The x-intercept is where the graph intersects the x-axis. Page 178

3. An x-intercept of a graph is the x-coordinate of a point where the graph intersects the x-axis. The y-coordinate of the x- intercept is always zero. The graph of y = 4x – 8 crosses the x-axis at (2, 0) and that point is the x-intercept. (2, 0) Finding x – intercept Page 179

4. The y-intercept of a graph is the y-coordinate of a point where the graph intersects the y-axis. The x-coordinate of the y-intercept is always zero. The graph of y = 3x + 4 crosses the y-axis at (0, 4) and that point is the y-intercept. (0, 4) Finding y- intercept Page 179

5. Example Use intercepts to graph 3x – 4y = 12. Solution The x-intercept is found by letting y = 0. The y-intercept is found by letting x = 0. The graph passes through the two points (4, 0) and (0, –3). Page 180

6. Example Complete the table for the graph of the equation x – y = 3. Solution Find corresponding values for the intercepts. Select one more point for the check point. The x-intercept is (3, 0). The y-intercept is (0, –3). XY(x,y) 0 0 Page 180 0

7. Graph 2x + 3y = 6. Graph the equation by drawing a line through the intercepts and checkpoint. Graphing Using Intercepts XY(x,y) 30(3,0) 02(0,2) -3 4 (-3,4) 6 -2 (6,-2) Page 180

8. Graph x + 3y = 0. Graph the equation by drawing a line through the intercepts and checkpoint. Graphing Using Intercepts XY(x,y) 00(0,0) 00 3 (3,-1) -3 1 (-3,1) Goes through the origin Page 180

9. Example A toy rocket is shot vertically into the air. Its velocity v in feet per second after t seconds is given by v = 320 – 32t. Assume that t ≥ 0 and t ≤ 10. a. Graph the equation by finding the intercepts. b. Interpret each intercept. Solution a. Find the intercepts. b. The t-intercept indicates that the rocket had a velocity of 0 feet per second after 10 seconds. The v-intercept indicates that the rocket’s initial velocity was 320 feet per second. Page 181

10. The equation of a horizontal line with y-intercept b is y = b. Horizontal Lines Page 181

11. Example Graph the equation y = 2 and identify its y-intercept. Solution The graph of y = 2 is a horizontal line passing through the point (0, 2), as shown below. The y-intercept is 2. Page 182

12. The equation of a vertical line with x-intercept k is x = k. Vertical Lines Page 183

13. Example Graph the equation x = 2, and identify its x-intercept. Solution The graph of x = 2 is a vertical line passing through the point (2, 0), as shown below. The x-intercept is 2. Page 183

14. Example Write the equation of the line shown in each graph. a.b. Solution a. The graph is a horizontal line. The equation is y = –1. b.The graph is a vertical line. The equation is x = –1. Page 184

15. DONE

16. Objectives Finding Intercepts Horizontal Lines Vertical Lines

17. Example Find an equation for a line satisfying the given conditions. a. Vertical, passing through (3, 4). b. Horizontal, passing through (1, 2). c. Perpendicular to x = 2, passing through (1,  2). Solution a. The x-intercept is 3. The equation is x = 3. b. The y-intercept is 2. The equation is y = 2. c. A line perpendicular to x = 2 is a horizontal line with y-intercept –2. The equation is y =  2. Page 184

18. Example Complete the table. Then determine the x-intercept and y-intercept for the graph of the equation x – y = 3. Solution Find corresponding values of y for the given values of x. x 33 11 013 y x 33 11 013 y 66 44 33 22 0 The x-intercept is (3, 0). The y-intercept is (0, –3). Page 180

19. Example Complete the table for the graph of the equation x – y = 3. Solution Find corresponding values for the intercepts. Select one more point for the check point. x 33 11 013 y 66 44 33 22 0 The x-intercept is (3, 0). The y-intercept is (0, –3). XY(x,y) 0 0 Page 180