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:

1. Write the equation: y = kx2. Substitute for x and y3. Solve for k4. Rewrite the equation substituting the value of

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. Write the equation y = kx2. Substitute for x and y 7 = k(35)3. Solve for k 7/35= k, or k = 1/54. Rewrite the equation with k y = 1/5x as the constant

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 = number of hours

1. y = kx2. 14.40 = k(30)3. 14.40/30 = k, or k = 0.48 Equation:

y = 0.48x

Practice Problems: Answers1. y = 28 when x = 7

Equation: y = 4x2. y = 30 when x = 8

Equation: y = x3. y = 400 when x = 125

Equation: y = x4. y = 630 when x = 175

Equation: y = x

Question… A manufacturer can create 6578 bolts

in two hours. How many bolts can they create in 5 hours?› Determine: What value is our x? Why?

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.

Practice Problems: Answers (Continued)5. Or you can set up a direct proportion:

=

And solve:2y = 32,890 2 2

y = 16,445