1. Variation and Proportion Indirect Proportion

2. The formula for indirect variation can be written as y=k/x where k is called the constant of variation. ***We can follow the same steps from direct variation!!   The steps to follow to solve a problem with indirect variation: 1. 1. Write the equation: y = k/x 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 indirect variation where y varies indirectly as x. One pair of values is y = 145 when x =.8. 1. 1. Write the equation: y = k/xy = k/x 2. 2. Substitute for x and y145 = k/.8 3. 3. Solve for k145(.8) = k, or k =116 4. 4. Rewrite the equation with k y = 116/x as the constant

4. Problem: The time (t) required to do a certain job varies inversely as the number (n) of people working (assuming all work at the same rate). It takes 4 hours for 20 people to wash and wax the floors in a building. Find the equation of variation.   y = time; x = number of people 1. 1. y = k/x 2. 2. 4 = k/20 3. 3. 420 = k, or k = 80   Equation: y = 80/x

5. Practice Problems: Answers 1. y = 25 when x = 3  Equation: y = 75/x 2. y = 45 when x = 2  Equation: y = 90/x 3. y = 80 when x =.7  Equation: y = 56/x 4. y =.8 when x = 4  Equation: y = 3.2/x

6. Practice Problems: Answers (Continued) 5. It takes 16 hours for 2 people to resurface a gym floor. How long would it take 6 people to do the job? 1. 1. Write the equation: y = k/xy = k/x 2. 2. Substitute for x and y16 = k/2 3. 3. Solve for k16(2) = k, or k =32 4. 4. Rewrite the equation with k y = 32/x as the constant