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Understanding Slope: Calculation and Interpretation of Line Equations

adrienne-burke avatar
adrienne-burke
28 diapositives · 426 Views · Nov 13, 2014

In this lecture, we delve into the concept of slope, defined as "rise over run," and explore its calculation based on two points on a line. Through practical examples, we demonstrate how to find the slope of lines passing through specific coordinates and verify these slopes graphically. Additionally, we discuss how to identify the slope and y-intercept from the equation of a line in the form Y = mx + b. By the end of this lecture, learners will be equipped with the skills to calculate and interpret slope effectively.

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  1. Unit 2 Lecture 16Slope Slope Lecture 16

  2. Objectives • Given two points, calculate the slope of the line through those two points • Given the equation of a line, identify the slope and y intercept. Lecture 16

  3. Slope Slope is rise over run. Lecture 16

  4. Slope Find the Slope of the line that passes through (6, -2) and (5, 7). Lecture 16

  5. Plot the points and verify the slope of -9 (6, -2) (5, 7) 4 2 2 4 -2 Lecture 16

  6. Plot the points and verify the slope of -9 (6, -2) (5, 7) 4 2 2 4 -2 Lecture 16

  7. Slope Find the Slope of the line that passes through (8, 2) and (4, -12). Lecture 16

  8. Plot the points and verify the slope of 3.5 (8, 2) (4, -12) 6 3 2 4 -3 -6 -9 -12 Lecture 16

  9. Plot the points and verify the slope of 3.5 (8, 2) (4, -12) 6 3 2 4 -3 -6 -9 -12 Lecture 16

  10. Slope Find the Slope of the line that passes through (2, 4) and (2, -5). Lecture 16

  11. Plot the points and verify the slope. (2, 4) (2, -5) 2 1 1 2 -1 Lecture 16

  12. Plot the points and verify the slope. (2, 4) (2, -5) 2 1 1 2 -1 Lecture 16

  13. Slope Find the Slope of the line that passes through (4, -3) and (-2, -3). Lecture 16

  14. Plot the points and verify the slope is 0. (4, -3) (-2, -3) 2 1 1 2 -1 -2 Lecture 16

  15. Plot the points and verify the slope is 0. (4, -3) (-2, -3) 2 1 1 2 -1 -2 Lecture 16

  16. Y= m x + b m = slope; b = y-intercept Lecture 16

  17. Y= m x + b m = slope; b = y-intercept Lecture 16

  18. Lecture 16

  19. (4, -8) (0, -5) 4 2 2 4 -2 Lecture 16

  20. Y= m x + b m = slope; b = y-intercept Lecture 16

  21. Y= m x + b m = slope; b = y-intercept Lecture 16

  22. y = 4x + 5 Lecture 16

  23. y = 4x + 5 8 (1, 9) 6 (0, 5) 4 2 1 2 -2 -4 Lecture 16

  24. y = 4x + 5 Lecture 16

  25. Solve for y in terms of x 3x + 2y = 6 3x + 2y = 6 2y = 6-3x Subtract 3x from both sides y = (6-3x)/2 Divide both sides by 2 Write in y = mx + b form Lecture 16

  26. Y= m x + b m = slope; b = y-intercept Lecture 16

  27. 3x + 2y = 6 Lecture 16

  28. (2, 0) (0, 3) 2 1 1 2 -1 Lecture 16