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Section 3.3

Section 3.3. More Graphing of Lines. Page 178. Finding Intercepts. The y -intercept is where the graph intersects the y -axis. The x -intercept is where the graph intersects the x -axis. Finding x – intercept. Page 179.

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Section 3.3

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  1. Section 3.3 • More Graphing of Lines

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

  3. Finding x – intercept Page 179 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)

  4. Finding y- intercept Page 179 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)

  5. Example Page 180 • 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).

  6. Example Page 180 • 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. 0 The x-intercept is (3, 0). The y-intercept is (0, –3).

  7. Graphing Using Intercepts Page 180 Graph 2x + 3y = 6. Graph the equation by drawing a line through the intercepts and checkpoint.

  8. Graphing Using Intercepts Page 180 Graph x + 3y = 0. Graph the equation by drawing a line through the intercepts and checkpoint. Goes through the origin

  9. Example Page 181 • 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.

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

  11. Example Page 182 • 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.

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

  13. Example Page 183 • 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.

  14. Example Page 184 • 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.

  15. DONE

  16. Objectives • Finding Intercepts • Horizontal Lines • Vertical Lines

  17. Example Page 184 • 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.

  18. Example Page 180 • 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. The x-intercept is (3, 0). The y-intercept is (0, –3).

  19. Example Page 180 • 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).

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