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Direct and Inverse Variation

Direct and Inverse Variation. Direct Variation. When y = k x for a nonzero constant k , we say that :. y varies directly as x, or y is proportional to x. The constant k is called the:. constant of variation, or constant of proportionality. Example 1.

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Direct and Inverse Variation

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  1. Direct and Inverse Variation • Direct Variation When y = k x for a nonzero constant k, we say that: yvaries directly as x, or y is proportional to x The constant k is called the: constant of variation, or constant of proportionality

  2. Example 1 When a weight is attached to a spring, the distance the spring stretches varies directly as the weight. If a weight of 5 pounds stretches the spring 10 inches, find the distance the spring will be stretched with a 7 pound weight. Let d = the distance the spring stretches w= the weight in pounds

  3. 1) Write the variation equation 3) Re-write the variation equation using the value of k 2) Use the given values to solve for k 4) Determine the distance for the given weight

  4. Conclusion The spring will travel a distance of 14 inches with the 7 pound weight. • Note: In the previous problem, you could have easily solved it in your head. The steps that were used are very important for future work when the problems are more difficult and/or contain other types of variation.

  5. Inverse Variation When y = k/x for a nonzero constant k, we say that: yvaries inversely as x, or y is inversely proportional to x The constant k is again called the: constant of variation, or constant of proportionality

  6. Example 2 Assume that y varies inversely as x and y = 3 when x = 12. Determine the value of y when x = 16

  7. 1) Write the inverse variation equation 3) Re-write the inverse variation equation using the value of k 2) Use the given values to solve for k 4) Determine the value of y for the given value of x

  8. END OF PRESENTATION Click to rerun the slideshow.

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