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.
Understanding Indirect Variation: Formula, Examples, and Applications
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Presentation Transcript
Variation and Proportion Indirect Proportion
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
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
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
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
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
