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DRILL

DRILL. Given each table write an equation to find “y” in terms of x. 2) Find the value of x:. Chapter 5 Analyzing Linear Equations. 5-1 Patterns and Slope Connection. Linear Patterns.

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DRILL

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  1. DRILL • Given each table write an equation to find “y” in terms of x. 2) Find the value of x:

  2. Chapter 5Analyzing Linear Equations 5-1 Patterns and Slope Connection

  3. Linear Patterns • In order for a pattern to be linear the common difference in “y” divided by the common difference in “x” must be the same for all given values.

  4. DRILL • Is this pattern linear? Why/Why Not • Solve for x:

  5. Slope • Slope is defined in numerous ways some of which are: 1) 2) Change in “y” Change in “x” 3)

  6. Slope Formula The formula for finding slope is: Where the coordinates of two points are (x1, y1) and (x2, y2)

  7. Types of Slopes Undefined _ + 0

  8. DRILL • Find the Slope Given the following points: • (2, 5) and (4, 13) • (-3, 3) and (7, -2) • (-4, 0) and (4, 24) • (5, 7) and (5, 13)

  9. 7.4 Slope Objectives: To find the slope of a line given two points on the line To describe slope for horizontal and vertical lines

  10. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Slope run rise

  11. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Example 1 Graph the line containing points (2,1) and (7,6) and find the slope. run rise

  12. Practice Graph the line containing these points and find their slopes. 1) (-2,3) (3,5) 2) (0,-3) (-3,2)

  13. Slope = Slope or

  14. Example 2 Find the slope of the line containing points (1,6) and (5,4).

  15. Practice Find the slope of the lines containing these points. 2) (-2,3) (2,1) 1) (2,2) (8,9) 3) (5,-11) (-9,4)

  16. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Slope of a Horizontal Line What about the slope of a horizontal line? What is the rise? 0 6 What is the run? The slope of ANY horizontal line is 0.

  17. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Slope of a Vertical Line What about the slope of a vertical line? What is the rise? 5 0 What is the run? The slope of ANY vertical line is undefined.

  18. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Example 1 Find the slope of the line y = -4.

  19. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Example 2 Find the slope of the line x = 7. The line has no slope.

  20. Practice Find the slopes, if they exist, of the lines containing these points. 1) (9,7) (3,7) 2) (4,-6) (4,0) 3) (2,4) (-1,5)

  21. 5 minutes Warm-Up Graph. Then find the slope. • y = 3x + 2 2) y = -2x +5

  22. 7.5.1 Equations and Slope Objectives: To find the slope and y-intercept of a line from an equation

  23. Slope-Intercept Equation Find the slope of the line y = 2x - 4. 8 y = 2x - 4 6 4 2 0 -4 6 8 -2 1 -2 -8 -6 -4 2 4 -2 rise: -4 2 0 -4 run: -2 -6 -8 The y-intercept is -4.

  24. Slope-Intercept Equation y = mx + b y = 4x + 8 y = 2x - 3 slope y-intercept slope = 4 y-intercept = 8 slope = 2 y-intercept = -3

  25. Example 1 Find the slope and y-intercept of the line y = -4x + 4. The slope is -4. The y-intercept is 4.

  26. Example 2 Find the slope and y-intercept of the line y = 5x - 7. The slope is 5. The y-intercept is -7.

  27. Practice Find the slope and y-intercept of each line. • y = x + 3 • y = -4x – 7 • y = 3x - 9

  28. Example 3 Find the slope and y-intercept of the line 3x + 4y = 12. 3x + 4y = 12 solve for y -3x -3x 4y = 12 – 3x 4 4 slope y-intercept = 3

  29. Practice Find the slope and y-intercept of each line. • y = -x - 3 2) 8x + 2y = 10 3) 3y – 6x = 12

  30. Homework p.326 #1-10,19-27 odds

  31. 4 minutes Warm-Up Find the slope and y-intercept. • y = 3x + 4 2) y = -2x - 8 3) 2x + 7y = 9 4) 4x = 9y + 7

  32. 7.5.2 Equations and Slope Objectives: To graph lines using the slope-intercept equation

  33. Example 1 Graph y = 3x + 2. 8 What is the slope of this line? 6 4 2 6 8 -2 -8 -6 -4 2 4 -2 What is the y-intercept? -4 b = 2 -6 -8

  34. Example 2 Graph 8 What is the slope of this line? 6 4 2 6 8 -2 -8 -6 -4 2 4 -2 What is the y-intercept? -4 b = -3 -6 -8

  35. Practice Graph each line. • y = 3x - 5 2) y = -2x + 4 3)

  36. Example 3 Graph 3x + 4y = 12. 3x + 4y = 12 solve for y -3x -3x 4y = -3x + 12 4 4

  37. Example 3 Graph 3x + 4y = 12. 8 6 4 2 6 8 -2 -8 -6 -4 2 4 -2 -4 slope -6 y-intercept -8

  38. Practice Graph each line. • 7x + 2y = 4 2) 5y – 10 = 4x

  39. Homework p.326 #29,31,37,39 *Use graph paper for the graphs

  40. 6 minutes Warm-Up 1. Find the slope of the line containing the points (-2,5) and (4,6). 2. Find the slope of the line y = x – 9. 3. Find the slope of the line 3y – 4x = 9.

  41. 7.6.1 Finding an Equation of a Line Objectives: To write an equation of a line using the slope-intercept equation

  42. The Slope-Intercept Equation y = mx + b slope y-intercept Create an equation of a line with a slope of -3 and a y-intercept of 4. y = -3x + 4 y = 4 – 3x 3x = 4 - y -4 = -y – 3x

  43. Example 1 Write an equation for the line with slope 3 that contains the point (-2,4) y = mx + b solve for b = 4 3 (-2) + b substitute simplify 4 = -6 + b +6 +6 10 = b y = 3x + 10

  44. Practice Write an equation for the given line that contains the given point and has the given slope. 1) (5,10); m = 4 2) (-3,8); m = 2

  45. Example 2 Write an equation for the line containing the points (1,5) and (2,8).

  46. Example 2 Write an equation for the line containing the points (1,5) and (2,8). y = mx + b substitute = 5 3 (1) + b simplify 5 = 3 + b -3 -3 2 = b y = 3x + 2

  47. Practice Write an equation for the line that contains the given points. 1) (-4,1) (-1,4) 2) (-3,5) (-1,-3)

  48. Homework p.331 #3,5,7,15,19

  49. 6 minutes Warm-Up 1. Write an equation for the line with slope -2 and containing the point (-3,0). 2. Write an equation for the line containing the points (0,0) and (4,2).

  50. 7.6.2 Finding an Equation of a Line Objectives: To write an equation of a line using the point-slope equation

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