Variation and Proportion

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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 = 7 when x = 35. Write the equation: y = kx y = kx Substitute for x and y 7 = k(35) Solve for k 7/35 = k, or k = 1/5 Rewrite the equation with k y = 1/5x as the constant

y = cost; x = number of hours y = kx 14 = k(30) 14/30 = k, or k = 7/15 Problem: The cost of operating a TV varies directly as the number (n) of hours it is in operation. It costs $14.00 to operate a standard size color TV continuously for 30 days. y = cost; x = number of hours y = kx 14 = k(30) 14/30 = k, or k = 7/15 Equation: y = 7/15x

Practice Problems: Answers y = 28 when x = 7 Equation: y = 4x y = 30 when x = 8 Equation: y = 15/4x y = 400 when x = 125 Equation: y = 16/5x y = 630 when x = 175 Equation: y = 18/5x

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 a proportion: 6578/2 = x/5 x = 16445