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A rate of change compares the change in one quantity relative to a change in another quantity Unlike slope, a rate of change is expressed in units (Example: km/h) Thus, speed is one example of a rate of change.

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Time (s) Average Distance (m) 20468101214161820 50 100 150 200 250 300 Cheetah (10,311) Professional Cyclist (10,165) Polar Bear (10,111) Olympic Sprinter (10,102) Average Running Distance vs. Time This graph shows the average distance, in meters, that each animal or person can run in 10s. Example

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Time (s) Average Distance (m) 20468101214161820 50 100 150 200 250 300 Cheetah (10,311) Professional Cyclist (10,165) Polar Bear (10,111) Olympic Sprinter (10,102) Average Running Distance vs. Time Visually compare the steepness of each graph, then determine the slope. Rank the slopes from greatest to least. Solutions: m (Cheetah) = 311/10 = 31.1 m (Cyclist) = 165/10 = 16.5 m (Bear) = 111/10 = 11.1 m (Sprinter) = 102/10 = 10.2

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Time (s) Average Distance (m) 20468101214161820 50 100 150 200 250 300 Cheetah (10,311) Professional Cyclist (10,165) Polar Bear (10,111) Olympic Sprinter (10,102) Average Running Distance vs. Time How do we find the speed of an object, animal, or person? Solutions: m (Cheetah) = 311/10 = 31.1 m (Cyclist) = 165/10 = 16.5 m (Bear) = 111/10 = 11.1 m (Sprinter) = 102/10 = 10.2 Speed = distance time Calculate the speed of each person or animal

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Time (s) Average Distance (m) 20468101214161820 50 100 150 200 250 300 Cheetah (10,311) Professional Cyclist (10,165) Polar Bear (10,111) Olympic Sprinter (10,102) Average Running Distance vs. Time What do you notice about the slope compared to the speed of each person or animal? They are the SAME!

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Thus, the rate of change between two variables is equal to the slope of the line when the two variables are graphed.

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A rate of change is typically calculated as: Rate of Change = change in dependent variable change in independent variable Subtract the two dependent variables Subtract the two independent variables

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Slope = change in y change in x Slope =

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Practice (homework): p. 268 #2, 3, 5, 7, 12, 14

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