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Slope

Slope. Special Section. SWBAT. Understand the meaning of the word slope Find the slope using two points on a line Determine the difference between positive slope, negative slope, zero slope Show lines that have the same slope are parallel. Understanding Slope.

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Slope

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  1. Slope Special Section

  2. SWBAT • Understand the meaning of the word slope • Find the slope using two points on a line • Determine the difference between positive slope, negative slope, zero slope • Show lines that have the same slope are parallel

  3. Understanding Slope Slopeis the ratio of the vertical change to the horziontal change In other words: Slope is the steepness of a line

  4. Mathematical Facts about Slope • Slope is denoted by the letter m • The vertical change (change in y) is called the rise • The horizontal change (change in x) is called the run

  5. Mr. V, what are you talking about?

  6. Find the Slope by Counting

  7. Find the Slope by Graphing:Find the slope of a line that goes through points (- 3, 5) and (2,1) • Plot the points

  8. To solve by graphing:Start at the left dot and count down till you’reeven with the right dot.

  9. To solve by graphing:Now count over till you reachthe right dot.

  10. Now Solve • We counted DOWN 4 spots, so we moved (– 4) units • We counted RIGHT 5 spots, so we moved 5 units • So our slope is: m = - 4/5

  11. Using Math to Find Slope When given two points (x1, y1) and (x2, y2) you can find the slope of a line by using the following formula:

  12. Slope Formula Continued

  13. Example of a Negative Slope

  14. GroupTry: Without graphing Find the Slope of a line through points (2,1) and (4,4) • Remember: • Hint: Identify (x1, y1) and (x2, y2)

  15. Group Try: Find the Slope of a line through points (2,1) and (4,4)

  16. Try on your own • Find the slope through the points (7, -4) and (9, 4) • Find the slope through the points (9, - 2) and (3, -5) Answer: m = 4 Answer: m = - ½

  17. Slope and Steepness • The greater the number, the steeper the slope (“faster” it moves up or down) • The smaller the number, the more gentle the slope (“slower” it moves up or down) m = 4 >> m =1/4 >>

  18. Classifying Slope • Positive Slope – Slants up from left to right (“uphill”) • Negative Slope – Slants down from left to right (“downhill”)

  19. Classifying Slope • Zero Slope – Line is horizontal (driving an a flat road) • Undefined Slope – Line is vertical (straight up and down) – Can you drive a car up a wall? NO!

  20. On Your Own:Label each slope as positive, negative, zero slope, or undefined

  21. One More Quick Note • Parallel lines have the same slope

  22. In Your Group • What is the slope of the line represented by the table of values below? Answer: m = 10

  23. Which Graph has a Positive Slope? A B A!! D C

  24. Which statement best describes the slope of the line graphed above? • The slope is – 6 • The slope is 2/3 • The slope is 3/2 • The slope is – 4 If you said: The slope is 2/3 You were WRONG! The slope is 3/2

  25. Which line has the greatest slope? This Guy!!! 

  26. Ticket to Leave • Write the slope formula using m, x1, y1, x2, y2 • Find the slope of the line that passes through the points (-2, 5) and (4, -5) • Describe the difference between the graph of a line with a positive slope and a negative slope • Describe the difference between the graph of a line with zero slope and undefined slope

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