Slope

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Slope

  1. 1. Drill 10-11/13 Copy the data then Find the mean 4, 6, 7, 9, 12, 15, 23, 30, 30 Put Both HW on the corner of your desk. You do not need your book today
  2. 2. Objective •SWBAT determine the slope of a line given two points and graph an equation given the slope and a point.
  3. 3. Slope • We have seen slope in a couple of different ways at this point: • Change in y over change in x: • Or: x y run rise
  4. 4. SLOPE EQUATION If you are given two points of the form: (x1 , y1) and (x2 , y2) The slope of the line containing those points is: 12 12 xx yy m
  5. 5. Examples • Determine the slope of the line containing the points (-3 , 5) and (4 , -2) m =
  6. 6. Examples • Determine the slope of the line containing the points (2 , -4) and (3 , -6) m =
  7. 7. Special Cases • If the slope of a line is equal to zero then the line is horizontal. • (2, -7) and (5, -7) m =
  8. 8. Special Cases • If the slope of a line is undefined (can’t divide by zero) then the line is vertical. • (-3, 4) and (-3, -2) m =
  9. 9. Now moving along… • We will now use the slope of an equation to graph. • Remember slope is: run rise
  10. 10. Using Slope to Move on a Graph •We can move from one point to another on a graph by using the slope written as a fraction. (if it is not a fraction we can make it one!)
  11. 11. Using Slope to Move on a Graph • Now we can think of it this way: • If the top number is positive, move up! If it is negative, move down. • The bottom number is always positive so we move right! rightmovefar toHow downorupmovefar toHow
  12. 12. Slope • We have seen slope in a couple of different ways at this point: • Change in y over change in x: • Or:
  13. 13. SLOPE EQUATION If you are given two points of the form: (x1 , y1) and (x2 , y2) The slope of the line containing those points is: 12 12 xx yy m
  14. 14. Examples • Determine the slope of the line containing the points (-3 , 5) and (4 , -2) m =
  15. 15. Examples • Determine the slope of the line containing the points (2 , -4) and (3 , -6) m =
  16. 16. Special Cases • If the slope of a line is equal to zero then the line is horizontal. • (2, -7) and (5, -7) m =
  17. 17. Special Cases • If the slope of a line is undefined (can’t divide by zero) then the line is vertical. • (-3, 4) and (-3, -2) m =
  18. 18. Study Guide #’s 1 – 9 1. For each problem, label x1, y1, x2, and y2. 2. Write the slope equation un- simplified. 3. Simplify the top and bottom. 4. Simplify the fraction if necessary
  19. 19. Determining a point… • Sometimes you will be given the slope of a line and three of the 4 values. • If this happened just set up your equation and solve for the unknown.
  20. 20. Example 1 • Given the slope and the information about the points determine the missing coordinate: • (10, r) and (3, 4); m = -2/7
  21. 21. Example 2 • Given the slope and the information about the points determine the missing coordinate: • (4, 8) and (r, 2); m = 2
  22. 22. Now moving along… • We will now use the slope of an equation to graph. • Remember slope is: run rise
  23. 23. Using Slope to Move on a Graph • Now we can think of it this way: • If the top number is positive, move up! If it is negative, move down. • The bottom number is always postitive so we move right! rightmovefar toHow downorupmovefar toHow

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