Variation and Proportion

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Direct Variation 5-2.

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Presentation transcript:

Variation and Proportion Direct Proportion

The formula for direct variation can be written as y=kx where k is called the constant of variation. The steps to follow to solve a problem with direct variation: Write the equation: y = kx Substitute for x and y Solve for k Rewrite the equation with k as the constant

Problem: Find an equation of direct variation where y varies directly as x. One pair of values is y = 35 when x = 5. Write the equation: y = kx y = kx Substitute for x and y 35 = k(5) Solve for k 7 = k Rewrite the equation with k y = 7x as the constant

y = cost; x = number of hours y = kx 60 = k(30) 60/30 = k, or k = 2 Problem: The cost of operating a TV varies directly as the number (d) days it is in operation. It costs $14.00 to operate a standard size color TV continuously for 30 hours. y = cost; x = number of hours y = kx 60 = k(30) 60/30 = k, or k = 2 Equation: y = 2x

Practice Problems: y = 28 when x = 7 y = 30 when x = 8

Practice Problems y = 400 when x = 125 y = 630 when x = 175

Practice Problems: Answers 9

Practice Problems: Answers (Continued) The number (b) of bolts a machine can make varies directly as the time it operates. It can make 6578 bolts in 2 hours. How many bolts can it make in 5 hours? Set up equation: Y=kx 6578 = 2k 6578/2 = k K = 3289 write equation: y = 3289x Then solve for new y y = 16445