1. Model Inverse and Joint Variation
Notes 9.1
Model Inverse and Joint Variation

2. The Equation of Direct Variation
The equation y = ax represents direct variation between x and y
y is said to vary directly with x.
Constant of Variation
The nonzero constant a is called the constant of variation. (Basically, a is slope)

3. Important: For a relation to be considered a direct variation,
THE RELATION MUST BE LINEAR AND PASS THROUGH THE ORIGIN (0, 0)

4. Inverse Variation
Two Variables x and y show inverse variation if they are related as follows:

5. Before classifying equations:
SOLVE FOR Y!

6. Classify as direct variation, inverse variation, or neither.

7. Write an inverse variation equation.
Step 1: write the general equation for inverse variation.
Step 2: substitute in the values.
Step 3: solve for a.
Step 4 Write the equation.

8. The variables x and y vary inversely, and y = 7 when x =4
The variables x and y vary inversely, and y = 7 when x =4. Write an equation that relates x and y. Then find y when x = -2.

9. The variables x and y vary inversely, and y = 3 when x = 4
The variables x and y vary inversely, and y = 3 when x = 4. Write an equation that relates x and y. Then find y when x = 2.

10. The variables x and y vary inversely, and y = -1 when x = 8
The variables x and y vary inversely, and y = -1 when x = 8. Write an equation that relates x and y. Then find y when x = 2.

11. The variables x and y vary inversely, and y = 12 when x =. 5
The variables x and y vary inversely, and y = 12 when x = .5. Write an equation that relates x and y. Then find y when x = 2.

12. Joint variation:
Occurs when a quantity varies directly with the product of two or more other quantities.
Examples:
(z varies jointly with x and y.)
(p varies jointly with q, r, and s.)

13. Write a joint variation equation.
Step 1: write a general joint variation equation.
Step 2: use the given values to find a.
Step 3: write the equation with a.
Step 4: substitute to find the missing variable.

14. The variable z varies jointly with x and y
The variable z varies jointly with x and y. Also, z = -75 when x = 3 and y = -5. Write an equation that relates x, y, and z. Then find z when x = 2 and y = 6.

15. The variable z varies jointly with x and y
The variable z varies jointly with x and y. Also, z = 7 when x = 1 and y = 2. Write an equation that relates x, y, and z. Then find z when x = -2 and y = 5.

16. The variable z varies jointly with x and y
The variable z varies jointly with x and y. Also, z = 24 when x = 4 and y = -3. Write an equation that relates x, y, and z. Then find z when x = -2 and y = 5.

17. Homework:
P , 40-45