1. Variation Objectives: Construct a Model using Direct Variation
Construct a Model using Inverse Variation
Construct a Model using Joint or Combined Variation

2. Variation: how one quantity varies in relation to another quantity
Direct Variation: y varies directly with x or y is directly proportional to x if there exists a constant k such that
Inverse Variation: y varies inversely as x or y is inversely proportional to x if there exists a constant k such that
Variation: how one quantity varies in relation to another quantity

3. Write a General Formula to describe each Variation
If a varies directly with b and a = 5 when b = 20. Find a when
b = 136.
If r is inversely proportional to the square root of y and r = 3/2
when y = 16. Find r when y = 6561

4. Joint Variation: z varies jointly as x and y or z is jointly proportional to x and y if there exists a constant k such that
Combined Variation: combinations of direct and/or inverse and/or joint variation that occur at the same time
Solving Variation Problems 1. Write an equation that describes the given English statement. 2. Substitute the given pair of values into the equation in step 1 and solve for k, the constant of variation. 3. Substitute the value of k into the equation in step Use the equation from step 3 to answer the problem’s question.

5. Write a General Formula to describe each Variation
If w varies jointly with m and the cube of z and w = 128 when m = 6
and z = 2. Find w when m = 4 and z = 3
If t is jointly proportional to the square root of a and b squared and
inversely proportional to c and t = 2 when a = 9, b = 5 and c = 150.
Find t when a = 16, b = 3 and c = 24.

6. 5. The distance that an object falls is directly proportional to the square of the time of the fall. If an object falls 64 feet in 2 seconds, how far will if fall in 5 seconds?
How long will it take the object to fall 784 feet?