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Understanding Indirect Variation: Formula, Examples, and Applications

This guide introduces the concept of indirect variation, where one variable varies inversely with another. The formula for indirect variation is expressed as y = k/x, with k representing the constant of variation. The explanation includes step-by-step procedures for solving problems involving indirect variation, with practical examples demonstrating the application of the formula. For instance, using given values to derive the constant k and rewriting the equation in terms of k. Practice problems are provided for reinforcement, along with solutions showcasing how to derive equations of indirect variation based on given scenarios.

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Understanding Indirect Variation: Formula, Examples, and Applications

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  1. Variation and Proportion Indirect Proportion

  2. The formula for indirect variation can be written as y=k/x where k is called the constant of variation.***We can follow the same steps from direct variation!!  • The steps to follow to solve a problem with indirect variation: • Write the equation: y = k/x • Substitute for x and y • Solve for k • Rewrite the equation with k as the constant

  3. Problem:Find an equation of indirect variation where y varies indirectly as x. One pair of values is y = 145 when x = .8. • Write the equation: y = k/x y = k/x • Substitute for x and y 145 = k/.8 • Solve for k 145(.8) = k, or k =116 • Rewrite the equation with k y = 116/x as the constant

  4. Problem:The time (t) required to do a certain job varies inversely as the number (n) of people working (assuming all work at the same rate). It takes 4 hours for 20 people to wash and wax the floors in a building. Find the equation of variation. • y = time; x = number of people • y = k/x • 4 = k/20 • 4•20 = k, or k = 80 • Equation: • y = 80/x

  5. Practice Problems: Answers • y = 25 when x = 3 • Equation: y = 75/x • y = 45 when x = 2 • Equation: y = 90/x • y = 80 when x = .7 • Equation: y = 56/x • y = .8 when x = 4 • Equation: y = 3.2/x

  6. Practice Problems: Answers (Continued) • It takes 16 hours for 2 people to resurface a gym floor. How long would it take 6 people to do the job? • Write the equation: y = k/x y = k/x • Substitute for x and y 16 = k/2 • Solve for k 16(2) = k, or k =32 • Rewrite the equation with k y = 32/x as the constant

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