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Introduction To Slope

Slope is a measure of steepness represented by the letter "m." Learn about types of slope - zero, negative, positive, undefined - and how to calculate it using the formula m = (y2 - y1) / (x2 - x1). Discover two methods for finding slope from equations, and how to interpret slopes and y-intercepts. With practical examples, grasp the concept of slope easily!

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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.

  5. The letter “m” is used to represent slope. Why?

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

  7. The formula may sometimes be written as m =∆y . ∆x What is ∆ ?

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

  9. (3, 4) and (-6, -2) m = -2 – 4 -6 – 3 m = -6 -9 m = ⅔

  10. What if the numerator is 0? What if the denominator is 0?

  11. If given an equation of a line, there are 2 ways to find the slope and y-intercept.

  12. One method is to write the equation in slope-intercept form, which is y = mx + b. slope y-intercept

  13. Find the slope and y-intercept of the following equations. y = 3x + ½ slope= 3 y-intercept = ½

  14. 3x + 5y = 10 First, solve the equation for y. 3x + 5y = 10 5y = -3x + 10 y = -3/5 x + 2 m= -3/5 b = 2

  15. Another method to find the slope if given an equation of a line is to write the equation in the form Ax + By = C. m = -A/B, b = C/B

  16. Find the slope and y-intercept of the following equations. A B C 8x + 11y = 7 m= -8/11 b = 7/11

  17. -6x = 2y + 14 First, rewrite the equation in the form Ax + By = C. -6x - 2y = 14 m= 6/-2 b = 14/-2 m= -3 b = -7

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

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

  20. The End

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