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Rate of Change in Mathematics

Explore the concept of rate of change and its applications in mathematics, including slope formula, average rate of change, and examples of linear functions. Learn how to find slopes between points and interpret positive and negative rates of change.

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Rate of Change in Mathematics

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  1. Average Rate of Change

  2. Rate of Change • Ratio describing how one quantity changes as another quantity changes • Slope can be used to describe it

  3. Rate of Change • Positive – increases over time • Negative – decreases over time

  4. Rate of Change • Linear functions have a constant rate of change, meaning values increase or decrease at the SAME rate over a period of time

  5. Rate of Change • Horizontal lines have 0 rate of change • Vertical lines have undefined rate of change

  6. Slope Formula

  7. Using the Slope Formula • Find the slope between the two given points: (2, 3) ( 4, -7)

  8. Using the Slope Formula • Find the slope between the two given points: (1, -4) ( 5, -6)

  9. Average Rate of Changeusing function notation

  10. Ex 3 Find the Average Rate of Change f(x) = -4x + 10 from [-1, 3]. m = -4

  11. Ex 1 Find the Average Rate of Change f(x) = 2x2 – 3 from [2, 4].

  12. Ex 2 Find the Average Rate of Change f(x) = 3x – 2 from [2, 5].

  13. Ex 4 Find the Average Rate of Change A. Find the rate of change from day 1 to 2. m = 11 B. Find the rate of change from day 2 to 5.

  14. Ex 5 Find the Average Rate of Change In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011. m = -5 What does this mean? It decreased 5 million households per year from 2008 – 11.

  15. Homework Rate of Change #1, 2 a, b, c, 3, 5, 6 problems

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