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

4. y = cost; x = number of hours y = kx 60 = k(30) 60/30 = k, or k = 2
Problem: The cost of operating a TV varies directly as the number (d) days it is in operation. It costs $14.00 to operate a standard size color TV continuously for 30 hours.
y = cost; x = number of hours
y = kx
60 = k(30)
60/30 = k, or k = 2
Equation:
y = 2x

5. Practice Problems:
y = 28 when x = 7
y = 30 when x = 8

6. Practice Problems
y = 400 when x = 125
y = 630 when x = 175

7. Practice Problems: Answers9

8. 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 equation:
Y=kx
6578 = 2k
6578/2 = k
K = write equation: y = 3289x
Then solve for new y y = 16445