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Inverse and Joint Variation Section 9.1 WHAT YOU WILL LEARN: 1. How to write and use inverse variation models. 2. How to write and use joint variation models. Oh Boy! Vocabulary We learned about direct variation in chapter 2. Two thing vary directly if when one goes up the other goes up or when one goes down the other goes down. Examples? Inverse variation is occurs when one thing goes up the other goes down. The equation we use for inverse variation is: k y k is called the constant of variation. x ,k 0 Classifying Direct and Inverse Variation • Tell whether x and y show direct, inverse variation or neither. 1. y x 5 2. y = x + 2 3. xy = 4 You Try • Do x and y show direct variation, inverse variation or neither. 1. xy = 4.8 2. x y 1 .5 Writing an Inverse Variation Equation • The variables x and y vary inversely, and y = 8 when x = 3. 1. Write an equation that relates x and y 2. Find y when x = -4 You Try • x and y vary inversely, and y = 6 when x = 1.5. • Write an equation that relates x and y. • Find y when x = 4/3 Word Problem • The speed of the current in a whirlpool varies inversely with the distance from the whirlpool’s center. The Lofoten Maelstrom is a whirlpool located off the coast of Norway. At a distance of 3 kilometers (3000 meters) from the center, the speed of the current is about 0.1 meter per second. Describe the change in the speed of the current as you move closer to the whirlpool’s center. You Try • The volume of gas in a container varies inversely with the amount of pressure. A gas has a volume of 75 in.3 at a pressure of 25lb/in2. Write a model relating volume and pressure. Checking for Inverse Variation • How can you tell when something is related inversely? • Example: W 2 4 6 8 10 H 9 4.5 3 2.25 1.8 Joint Variation Joint variation occurs when a quantity varies directly as the product of two or more other quantities. For instance, if z=kxy where k does not equal zero, then z varies jointly with x and y. Joint Variation Example • The variable z varies jointly with x and y. Write an equation relating x, y and z. Then find z when x = -4 and y = 7. Use z = kxy x = 3, y = 8, z = 6 You Try • Homework problem #40. The variable z varies jointly with x and y. Write an equation relating x, y and z. Then find z when x = -4 and y = 7. Use z = kxy x = -12 y = 4 z = 2 Types of Variation • Direct y = kx • Inverse k y x • Joint y = kxy Homework Page 537, 22-38 even, 40-44 even, 48-50 all