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6-1 Slope

6-1 Slope. Slope is a measure of steepness. The letter “m” is used to represent slope. 4 Types of Slope. Zero. Negative. Positive. Undefined or No Slope. Slope is sometimes referred to as the “constant rate of change” between 2 points.

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6-1 Slope

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  1. 6-1 Slope

  2. Slope is a measure of steepness.

  3. The letter “m” is used to represent slope.

  4. 4 Types of Slope Zero Negative Positive Undefined or No Slope

  5. Slope is sometimes referred to as the “constant rate of change” between 2 points.

  6. The constant rate of change can be written as = Change in the Dependent Variable Change in the Independent Variable Dependent = Y value Independent = X value

  7. Since slope is a constant rate of change, always look for a number or pattern that repeats. So what pattern do you see that the y-values follow? What happens every time? That’s the slope of the table!

  8. If given 2 points on a line, you may find the slope using the formula m = y2 – y1 x2 – x1 (the change in y divided by the change in x)

  9. The formula may sometimes be written as m =∆y . ∆x What does ∆ stand for? change

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

  11. (3, 4) and (-6, -2) m = -2 – 4 -6 – 3 m = y2 – y1 x2 – x1 m = -6 -9 m = ⅔

  12. (0, -5) and (4, 3) m = 3 – -5 4 – 0 m = y2 – y1 x2 – x1 m = 8 4 m = 2 or 2/1

  13. What if the numerator is 0? m = 0 What if the denominator is 0? m = undefined or no slope

  14. Slope is also found by m = rise run

  15. If given the graph of a line, find the slope by using the “triangle” method to find the rise over run.

  16. rise = 4 m= rise run run = 5 m= 4/5

  17. rise = 2 m= rise run run = -5 m= - 2/5

  18. Recap today’s lesson: • Slope is the steepness of a line or constant rate of change. • m represents slope • Slope can be found different ways • Rise over Run • Y2 – Y1 • X2 – X1

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