1. LESSON 12-1 INVERSE VARIATION
Algebra I
Mr. Kohls

2. Definition: inverse variation
An inverse variation is an equation in the form xy = k, where k does not equal 0.
As with direct variation, k is the constant.
**Remember Direct Variation: ( y = kx)

3. What does an inverse variation graph look like?

4. So what is inverse variation?
In an inverse variation, the values of the two variables change in an opposite manner - as one value increases, the other decreases.

5. Can you give me an example?
A biker traveling at 8 mph can cover 8 miles in 1 hour. If the biker's speed decreases to 4 mph, it will take the biker 2 hours to cover the same distance. As his speed decreases, the time increases.

6. Write an Equation Given a Point
Suppose y varies inversely with x and y = 7 when x = 5. Write an equation for the inverse variation.
xy = k Use general form of inverse variation.
5(7) = k Substitute the values you know for x and y.
35 = k Solve for k.
xy = 35 Write an equation substituting 35 for k in xy = k.
The equation is xy = 35.

7. Write an Equation Given a Point
Suppose y varies inversely with x and y = -2 when x = 3. Write an equation for the inverse variation.
xy = k Use general form of inverse variation.
3(-2) = k Substitute the values you know for x and y.
-6 = k Solve for k.
xy = -6 Write an equation substituting -6 for k in xy = k.
The equation is xy = -6.

8. Find the missing variable.
y varies inversely with x. If y = 14 when x = 2, find x when y = 4

9. Find the missing variable.
y varies inversely with x. If y = 11 when x = 5, find x when y = 5.5

10. Solve for the missing measurement
The volume V of gas varies inversely to the pressure P. The volume of a gas is 120 cm3 under pressure of 5 kg/cm2. What will be its volume under pressure of 40 kg/cm2?

11. Tell whether the data in each table is a direct variation, or an inverse variation. Then write and equation to model the data. x 2 7 10 y 35 x 2 6 9 y 18 27