1. 8-1 Direct, Inverse, and Joint Variation Some relationships in mathematics can be described as examples of direct variation. This means that y is a multiple of x. To express a direct variation, we say that y varies directly as x. In other words, as x increases, y increases or decreases at a constant rate.

2. Ex1: a) If y varies directly as x and y=9 when x =-15, find y when x=21. Think of these as y 1, and x 1, Think of these as y 2, and x 2,

3. b) If y varies directly as x and y=-15 when x=5, find y when x=3. y 1, and x 1,

4. Ex 2) If y varies inversely as x and y=4 when x=12, find y when x=5. y 1, and x 1, y 2, and x 2,

5. b) If y varies inversely as x and y=-14 when x=12, find x when y=21.

6. Another type of variation is joint variation. This type of variation occurs when one quantity varies directly as the product of two or more other quantities.

7. Example 3: a)Suppose y varies jointly as x and z. Find y when x=8 and z=3, if y=16 when z=2 and x=5. Think of these as y 1, x 1, z 1 and these as y 2, z 2, x 2 Now plug into the formula and solve.

8. b) Suppose y varies jointly as x and z. Find y when x=10 and z=5, if y=12 when z=8 and x=3.

9. CLASSWORK 1.If y varies inversely as x and y = -12 when x = 5, find x when y = -7 2. If y varies directly as x and y = 9 when x = 6, find y when x = 8. 3. Suppose y varies jointly as x and z. Find y when x = 5 and z = 3, if y = 18 when x = 3 and z = 5.