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Introduction To Slope

Learn about the different types of slope, how to calculate slope using formulas, interpret slopes from graphs, and create graphs with specific slopes. Also, discover the slope of horizontal and vertical lines and find slope using ratio tables and variables.

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Introduction To Slope

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  1. Introduction To Slope

  2. Slope is a measure of Steepness.

  3. Types of Slope Zero Negative Positive Undefined or No Slope

  4. Slope is sometimes referred to as the “rate of change” between 2 points. • The letter “m” is always used to represent slope.

  5. A. FORMULA

  6. If given 2 points on a line, you may find the slope using the Formula… m = y2 – y1 x2 – x1

  7. NOTE: The formula may sometimes be written as m =∆y . ∆x

  8. Slope can be expressed in some other different ways:

  9. 1.) Find the slope of the line through the points (3,7) and (5, 19). x1 y1 x2 y2 m = 19 – 7 5 – 3 m = y2 – y1 x2 – x1 m = 12 2 m = 6

  10. 2) Find the slope of the line that passes through the points (-2, -2) and (4, 1). When given points, it is easier to use the formula!

  11. 3) Find the slope of the line that goes through the points (-5, 3) and (2, 1).

  12. 4) Find the slope of the line that passes through (3, 5) and (-1, 4). • 4 • -4 • ¼ • - ¼

  13. B. Determine the slope of a line with a graph

  14. When given the graph, it is easier to apply “rise over run”.

  15. Determine the slope of the line. Start with the lower point and count how much you rise and then how much you run to get to the other point! rise 3 = = run 6 6 • This is called the Triangle Method • The slope is positive since the line is increasing 3

  16. Determine the slope of the line shown.

  17. Determine the slope of the line. Find points on the graph. Use two of them and apply rise over run. 2 1 The line is decreasing (slope is negative).

  18. What is the slope of a horizontal line? The line doesn’t rise! All horizontal lines have a slope of 0.

  19. What is the slope of a vertical line? The line doesn’t run! All vertical lines have an undefined slope.

  20. C. Creating a Graph

  21. Draw a line through the point (2,0) that has a slope of 3. 1. Graph the ordered pair (2, 0). 2. From (2, 0), apply rise over run (write 3 as a fraction). 3. Plot a point at this location. 4. Draw a straight line through the points. 1 3

  22. Ratio Tables • Sometimes, instead of giving coordinate points, they will give a ratio table. • You can still find the slope from this by using them as coordinate points.

  23. D. Finding the Slope with Variables

  24. The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r. To solve this, plug the given information into the formula

  25. To solve for r, simplify and write as a proportion. Cross multiply. 4(4 – r) 1(-4) =

  26. Simplify and solve the equation.1(-4) = 4(4 – r) -4 = 16 – 4r -16 -16 -20 = -4r -4 -4 5 = r The ordered pairs are (5, 6) and (4, 2)

  27. The End

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