LESSON 12-1 INVERSE VARIATION Algebra I Ms. Turk Algebra I Ms. Turk.

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Presentation transcript:

LESSON 12-1 INVERSE VARIATION Algebra I Ms. Turk Algebra I Ms. Turk

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. 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.

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.

In this slide show, you will learn how to solve inverse variations!

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. 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. 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.