Variation and Proportion Direct Proportion The formula for
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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: Ø 1. 2. 3. 4. Write the equation: y = kx Substitute for x and y Solve for k …(use division) 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. 1. 2. 3. 4. Write the equation: y = kx Substitute for x and y Solve for k Rewrite the equation with k as the constant y = kx 7 = k(35) 7/35 = k, or k = 1/5 y = 1/5 x or y =. 2 x
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. Ø y = cost; x = number of hours 1. 2. 3. y = kx 14 = k(30) 14/30 = k, or k = 7/15 Ø Equation: l y = 7/15 x
Practice Problems: Answers 1. y = 28 when x = 7 Ø 2. y = 30 when x = 8 Ø 3. Equation: y = 15/4 x or y = 3. 75 x y = 400 when x = 125 Ø 4. Equation: y = 4 x Equation: y = 16/5 x or y = 3. 2 x y = 630 when x = 175 Ø Equation: y = 18/5 x or y = 3. 6 x
Practice Problems: Answers (Continued) 5. 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? Ø Set up a proportion: Ø 6578/2 = x/5 Ø x = 16445
