1. U SING D IRECT AND I NVERSE V ARIATION D IRECT V ARIATION The variables x and y vary directly if, for a constant k, k  0. y = kx, Objective Lesson 11.3 Direct Variation: The values of x and y increase or decrease together

2. INDIRECT VARIATION The variables x and y vary inversely, if for a constant k, k  0. Inverse variation: As the x increases the y decreases.

3. S OLUTION 2 = k EX: When x is 2, y is 4. Find an equation that relates x and y directly. Replace x with 2 and y with 4 Write equation in y = kx form y = 2x. y = kx Direct variation 4 = k2 Solve for k

4. 8 = k When x is 2, y is 4. Find an equation that relates x and y inversely. Replace x with 2 and y with 4 Solve for k Write equation in form Inversely related

5. Inverse Variation: 8 x y =y = x y = 2x 1234 Make a table using y = 2x and y =. 8 x Direct Variation: Make a table and graph each equation 2 4 6 8 8 4 8 3 2

6. Inverse Variation: Direct Variation: y = 2x Direct y = 2x Inverse 8 x y =y = Graph y = 2x and

7. Inverse and Direct Variation State whether the variables have direct or an inverse variation. 1)The Area “A” of a rectangle changes as the Base “B” Increases. Directly: They both go up together. 2) The amount of gas in the tank and the number of miles driven. Inversely: As miles increase, gas in the tank decreases