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Direct Variation

Direct Variation. 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

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Direct Variation

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  1. Direct Variation

  2. The formula for direct variation can be written as y=kxwhere 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 substituting the value of k as the constant

  3. 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 • Substitute for x and y7 = k(35) • Solve for k7/35= k, or k = 1/5 • Rewrite the equation with k y = 1/5x as the constant

  4. Problem:The cost of operating a TV varies directly as the number of hours it is in operation. It costs $14.40 to operate a standard size color TV continuously for 30 hours. • y = cost; x = numberofhours • y = kx • 14.40= k(30) • 14.40/30= k, or k = 0.48 • Equation: y = 0.48x

  5. 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

  6. Practice Problems: Answers (Continued) 5. Follow the steps above: • y = kx • 6578 = k(2) • 6578/2 = k or 3289 • y = 3289x Solve the equation for the new y: y = 3289(5) y = 16,445 The machine can make 16,445 bolts in 5 hours.

  7. Practice Problems: Answers (Continued) 5. Or you can set up a direct proportion: • 6578/2 = x/5 And solve: 2x = 32,890 2 2 • x = 16,445

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