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Understanding Slope and Rate-of-Change in Mathematics

Learn about slope as the ratio of vertical to horizontal change, types of slopes (positive, negative, zero, undefined), parallel and perpendicular lines, and calculating rate-of-change using real-life examples.

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Understanding Slope and Rate-of-Change in Mathematics

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  1. p86 3-11, 18-23, 25,26, 41 Chapter 2.2 Slope & Rate-of-Change

  2. Slope The ratio of the vertical change of a line to the horizontal change. Rise over run. Run Rise

  3. Find slope

  4. Find slope

  5. Types of Slopes Positive Slope Negative Slope

  6. HOY VUX • H - horizontal • O - M=0 • Y - Y=(some number) • V - Vertical • U - M=Undefined • X - X=(some number)

  7. HOY VUX Zero Slope Undefined Slope

  8. examples

  9. examples

  10. examples

  11. Parallel & Perpendicular • Parallel – Lines that never cross. Have the same slopes • Perpendicular – Lines intersect at one point. Slopes are negative reciprocals of each other.

  12. examples • Parallel

  13. examples • Perpendicular

  14. Are each set of lines parallel, perpendicular or neither?

  15. Are each set of lines parallel, perpendicular or neither?

  16. Are each set of lines parallel, perpendicular or neither?

  17. Rate-of-Change • Rate-of-Change – To calculate a rate of change just find the slope of the values. • Units – Expressed as the ratio of the units of the y-value over the units of the x-value.

  18. Example If the population of a city changed from 5,000 people in 1990 to 3,000 people in 2000 what was the rate-of-population change for the city?

  19. Assignment • p86 3-11, 18-23, 25,26, 41

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