Stair on slope of a line

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Lesson on slope of a line

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Stair on slope of a line

  1. 1. SLOPE OF A LINE When you hear the word “slope” what comes to mind?
  2. 2. Slope of a Line The slope of a line measures the steepness of a line. You have probably heard teachers say “rise over run”. • Rise means how many units you move up or down from point to point. On a graph that would be a change in the y-values. • Run means how many units you move left or right from point to point. On a graph that would be a change in the x-values. rise slope run c
  3. 3. Positive Slope Note that a line y=0.5x+3 6 with a positive 5 slope increases as 4 3 you read the 2 graph from left to 1 0 right. -6 -4 -2 0 2 4 6 Slope-Intercept Form c
  4. 4. Negative Slope y=-3x-2 6 Note that a line 4 with a negative 2 slope decreases as -3 -2 -1 0 0 1 2 3 -2 you read the -4 graph from left to -6 right -8 -10 Slope-Intercept Form c
  5. 5. Zero Slope y=0x+1 Note that a line 1.2 with a slope of 1 zero is horizontal 0.8 0.6 as you read the 0.4 graph from left to 0.2 right 0 -3 -2 -1 0 1 2 3 Slope-Intercept Form c
  6. 6. Undefined Slope X = -2 5 When a line is 4 vertical, the slope is 3 undefined. A 2 vertical line cannot 1 be written in Slope- 0 -2.5 -2 -1.5 -1 -0.5 0 Intercept Form. -1 -2 -3 c
  7. 7. Slope Formula Given Two Points You are now going to calculate the slope of a line and compare it to the Slope-Intercept Equations on the four previous slides. Given two points, x y and x y , calculate the slope. 1, 1 2 , 2 m = rise = change in y = x 2 - y1 run change in x y - x1 2 c
  8. 8. Positive Slope Given Two Points: A= - 4,1 B= 2,4 m = 4 - 1 = 3 = 1 = 0.5 2 - -4 6 2 Note that the slope of the line passing through points A and B is 0.5. Compare this to the first graph by clicking the arrow.
  9. 9. Negative Slope Given Two Points: A= - 2,4 B= 1,-5 m = -5 - 4 = -9 = -3 1 - -2 3 Note that the slope of the line passing through points A and B is -3. Compare this to the second graph by clicking the arrow.
  10. 10. Zero Slope Given Two Points: A= - 2,1 B= 2,1 m = 1- 1 = 0 = 0 2 - -2 4 Note that the slope of the line passing through points A and B is 0. Compare this to the third graph by clicking the arrow.
  11. 11. Undefined Slope Given Two Points: A= - 2,4 B= 4,-7 m= -2 - 4 = -6 = undefined -2 - -2 0 Note that the slope of the line passing through points A and B is undefined. Compare this to the fourth graph by clicking the arrow.
  12. 12. Checking for Understanding The Slope-Intercept Form of a line is y=mx+b where m is the slope of the line and b is the y-intercept of the line. Did you notice the relationship between the slopes that were calculated and the graphs of the equations? Now continue with the practice problems.
  13. 13. Practice Problems Given the equation, what is the slope of the line? y 2x 7 A) 7 C) 3 3 2 B) 2 D) X 3
  14. 14. That response is incorrect, the correct 2 response is 3 . Remember that when an equation is in Slope-Intercept form, y=mx+b, the slope is the coefficient of x. Don’t be discouraged! Let’s try another problem.
  15. 15. That is Correct!
  16. 16. Practice Problems Calculate the slope of the line that passes through the given points. A= -5,2 A) -1 C) 5 B= 4,-7 B) 5 D) 9 9 5
  17. 17. That is incorrect. The correct response is A. Refer back to slide 9 if you need to review how to calculate the slope of a line using the slope formula. -7 - 2 -9 m= = = -1 4 - -5 9
  18. 18. That is correct!
  19. 19. Determine the slope of the line from the given graph. y-axis 4 1 3 A) -2 B) 2 2 1 1 0 C) 2 D) -2 -1 -1 0 1 2 3 4 2 -2 -3 -4 -5 -6
  20. 20. That is correct!
  21. 21. That is incorrect. If you start at the point (0,-3) and move to the point(1,-1), the movement was 2 units up and 1 unit right which means the slope is 2 which is 2. 1
  22. 22. Conclusion Today you have learned to find the slope of a line by reading a graph, using the slope formula, and by knowing that in the slope-intercept formula, m is the slope. In our next lesson, we will continue our study of linear functions. Cheers!
  23. 23. Positive Slope Note that a line y=0.5x+3 6 with a positive 5 slope increases as 4 3 you read the 2 graph from left to 1 0 right. -6 -4 -2 0 2 4 6 Slope-Intercept Form
  24. 24. Negative Slope y=-3x-2 6 Note that a line 4 with a negative 2 slope decreases as -3 -2 -1 0 0 1 2 3 -2 you read the -4 graph from left to -6 right -8 -10 Slope-Intercept Form
  25. 25. Zero Slope y=0x+1 Note that a line 1.2 with a slope of 1 zero is horizontal 0.8 0.6 as you read the 0.4 graph from left to 0.2 right 0 -3 -2 -1 0 1 2 3 Slope-Intercept Form
  26. 26. Undefined Slope X = -2 5 When a line is 4 vertical, the slope is 3 undefined. A 2 vertical line cannot 1 0 be written in Slope- -2.5 -2 -1.5 -1 -0.5 0 -1 Intercept Form. -2 -3
  27. 27. Nice work!

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