1. Variation and Proportion
Direct Proportion

2. 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

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 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

4. 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

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)
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