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Chapter 7 Section 5

Chapter 7 Section 5. Graphing Linear Equations. What You’ll Learn. You’ll learn to graph linear equations by using the x- and y- intercepts or the slope and y intercept. Why It’s Important. Rates Linear graphs are helpful in showing phone costs. Example 1.

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Chapter 7 Section 5

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  1. Chapter 7 Section 5 Graphing Linear Equations

  2. What You’ll Learn You’ll learn to graph linear equations by using the x- and y- intercepts or the slope and y intercept.

  3. Why It’s Important Rates Linear graphs are helpful in showing phone costs.

  4. Example 1 Determine the x-intercept and y-intercept of the graph of each equation. Then graph the equation. 5y – x = 10 To find the x-intercept, let y = 0. 5(0) – x = 10 - x = 10 -1 -1 x = -10 (-10,0) To find the y-intercept, let x = 0 5y – 0 = 10 5y = 10 5 5 y = 2 (0,2)

  5. Example 1: Continued • The x-intercept is -10, and the y-intercept is 2. This means that the graph intersects the x- axis at (-10, 0) and the y-axis at (0, 2). • Graph these ordered pairs. • Then draw the line that passes through these points.

  6. (0, 2) Example 1: Continued Y 8 7 6 5 4 3 2 1 0 • Graph: 5y – x = 10 (-10, 0) x -15 -14 -13-12 -11 -10 9 -8 -7 -6 -5 -4 -3 -2 -1

  7. Example 2 Determine the x-intercept and y-intercept of the graph of each equation. Then graph the equation. 2x – 4y = 8 To find the x-intercept, let y = 0. 2x – 4(0) = 8 2x = 8 2 2 x = 4 (4, 0) To find the y-intercept, let x = 0 2(0) – 4y = 8 -4y = 8 -4 -4 y = -2 (0,-2)

  8. Example 2: Continued • The x-intercept is 4, and the y-intercept is -2. This means that the graph intersects the x- axis at (4, 0) and the y-axis at (0, -2). • Graph these ordered pairs. • Then draw the line that passes through these points.

  9. (4, 0) Example 2: Continued 2 1 0 -1 -2 -3 -4 -5 • Graph: 2x – 4y = 8 x 1 2 3 4 5 6 7 8 (0, -2) Y

  10. How to Check Your Work • Look at the graph. • Choose some other point on the line and determine whether it is a solution of 2x – 4y = 8. • Try (2, -1) 2x – 4y = 8 2(2) – 4(-1) = 8 4 + 4 = 8 8 = 8

  11. Your Turn Determine the x-intercept and y-intercept of the graph of each equation. Then graph the equation. x + y = 2

  12. x + y = 2 (0, 2) (2, 0)

  13. Your Turn Determine the x-intercept and y-intercept of the graph of each equation. Then graph the equation. 3x + y = 3

  14. 3x + y = 3 (0, 3) (1, 0)

  15. Your Turn Determine the x-intercept and y-intercept of the graph of each equation. Then graph the equation. 4x – 5y = 20

  16. 4x – 5y = 20 (5, 0) (0, -4)

  17. Example 3 To mail letter in 2000, it cost $0.33 for the first ounce and $0.22 for each additional ounce. This can be represented by y = 0.33 + 0.22x. Determine the slope and y-intercept of the graph of the equation. y = mx + b y = 0.22x + 0.33 The slope is 0.22, and the y-intercept is 0.33. So the slope represents the cost per ounce after the first ounce, and the y-intercept represents the cost of the first ounce of mail.

  18. Example 4 Determine the slope and y-intercept of the graph of 10 + 5y = 2x. Write the equation in slope-intercept form to find the slope and y-intercept 10 + 5y = 2x 10 + 5y = 2x -10 = -10 5y = 2x – 10 5 5 y = ⅖x – 2 The slope is ⅖, and the y-intercept is -2.

  19. Your Turn Determine the slope and y-intercept. y = 5x + 9 m = 5, b = 9

  20. Your Turn Determine the slope and y-intercept. 4x + 3y = 6 m = - 4/3 , b = 2

  21. Example 5 Graph each equation by using the slope and y-intercept y = ⅔x – 5 y = mx + b y = ⅔x + (-5) The slope is ⅔, and the y-intercept is -5. Graph the point at (0, -5). Then go up 2 units and right 3 units. This will be the point at (3, -3). Then draw the line through points at (0, -5) and (3, -3).

  22. Example 5: Continued 3 (3, -3) 2 (0, -5)

  23. Example 5: Check • The graph appears to go through the point at (6, -1) . Substitute (6, -1) into y = ⅔x + (-5). y = ⅔x + (-5) -1 = ⅔(6) + (-5) -1 = 4 – 5 -1 = -1 Replace x with 6 and y with -1.

  24. Example 6 Graph each equation by using the slope and y-intercept. 3x + 2y = 6 First, write the equation in slope intercept form. 3x + 2y = 6 -3x = -3x 2y = -3x + 6 2 2 y = -3⁄₂x + 3 The slope is -3⁄₂ and the y-intercept is 3.

  25. Example 6: Continued • Graph the point (0, 3). • Then go up 3 units and left 2 units. • This will be the point at (-2, 6). • Then draw a line through (0, 3) and (-2, 6). • You can check your answer by substituting the coordinates of another point that appears to lie on the line, such as (2, 0).

  26. Example 6: Graph -2 (-2, 6) 3 (0, 3)

  27. Your Turn Graph each equation by using the slope and y-intercept. y= ½x + 3

  28. Answer (2, 4) (0, 3) y = ½x + 3

  29. Your Turn Graph each equation by using the slope and y-intercept. x + 4y = -8

  30. Answer (0, -2) (-4, -1) x + 4y = -8

  31. Something to Memorize • The graph of a horizontal line has a slope of 0 and no x-intercept. • The graph of a vertical line has an undefined slope and no y-intercept.

  32. Example 7 Graph each equation. y = 4 y = mx + b y = 0x + 4 No matter what the value of x, y = 4. So, all ordered pairs are of the form (x, 4). Some examples are (0, 4) and (-3, 4).

  33. 0 Example 7: Continued (-3, 4) (0, 4)

  34. Example 8 Graph each equation. x = -2 Slope is undefined, y- intercept: none No matter what the value of y, x = -2. So, all ordered pairs are of the form (-2, y). Some examples are (-2, -1) and (-2, 3).

  35. Example 8 (-2, 3) (-2, -1)

  36. Your Turn Graph each equation. y= -1

  37. y = -1 Answer

  38. Try This One Graph each equation. x = 3

  39. Answer x = 3

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