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Understanding Rates and Slopes: Application in Graphing and Equations

Learn about rates and slopes in mathematics, including how to calculate rates of change, graph speed versus time, find slopes of lines, work with horizontal and vertical lines, and understand slopes as speeds in real-life scenarios.

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Understanding Rates and Slopes: Application in Graphing and Equations

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  1. Chapter 3 Section 3 Rates and slopes

  2. Rate • A rate is a ratio that indicates how two quantities change with respect to each other. For example, if you walked 20 meters (m) in 5 seconds (s), your rate would be:

  3. Rate of Change • You park your 1999 Toyota Corolla on Fickle Hill and the parking break fails (again) and the car starts to roll down the hill. The car speeds up at a constant rate of 10 meters per second every second, that is it is accelerating. Sketch the graph of speed of the object versus time.

  4. y y2 y1 x x1 x2 Slope of a Line

  5. Slope of a Line

  6. Your Turn

  7. Use the Slope Formula

  8. Graph using the given point and slope.

  9. Horizontal Line • The equation of a horizontal line is given by: • The slope is 0.

  10. Find the Slope

  11. Vertical Line • The equation of a vertical line is given by: • The slope is undefined

  12. Find the Slope

  13. Slope as Speed

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