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: 1. 1. Write the equation: y = kx 2. 2. Substitute for x and y 3. 3. Solve for k 4. 4. 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 = 7. 1. 1. Write the equation: y = kxy = kx 2. 2. Substitute for x and y35 = k(7) 3. 3. Solve for k5= k 4. 4. Rewrite the equation with k y = 5x as the constant

4. Problem: The cost of operating a TV varies directly as the number (n) of hours it is in operation. It costs $60.00 to operate a standard size color TV continuously for 30 days.   y = cost; x = number of hours 1. 1. y = kx 2. 2. 60 = k(30) 3. 3. 60/30 = k, or k = 2   Equation: y = 2x

5. Practice Problems: Answers 1. y = 28 when x = 7  Equation: y = 4x 2. y = 30 when x = 8  Equation: y = 15/4x 3. y = 400 when x = 125  Equation: y = 16/5x 4. y = 630 when x = 175  Equation: y = 18/5x

6. 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?  Set up a proportion:  6578/2 = x/5  x = 16445