LESSON 12-1 INVERSE VARIATION

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Presentation transcript:

LESSON 12-1 INVERSE VARIATION Algebra I Mr. Kohls

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)

What does an inverse variation graph look like?

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.

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.

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.

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.

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

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

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?

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