Direct, Inverse and Joint Variation

Direct Variation y varies directly as x if there is some nonzero constant k such that y = kx. k is called the constant of variation y varies directly as x if there is some nonzero constant k such that y = kx. k is called the constant of variation

Example If y varies directly as x and y = 9 when x is -15, find y when x = 21. If y varies directly as x and y = 9 when x is -15, find y when x = 21.

Inverse Variation y varies inversely as x if there is some nonzero constant k such that xy = k or y = k/x y varies inversely as x if there is some nonzero constant k such that xy = k or y = k/x

Example If y varies inversely as x and y = 4, when x = 12, find y when x = 5. If y varies inversely as x and y = 4, when x = 12, find y when x = 5.

Joint Variation y varies jointly as x and z if there is some number k such that y = kxz, where and y varies jointly as x and z if there is some number k such that y = kxz, where and

Example The area A of a trapezoid varies jointly as the height h and the sum of its bases b1 and b2. Find the equation of joint variation if A = 48 in^3, h = 8 in., b1 = 5 in. and b2 = 7 in. The area A of a trapezoid varies jointly as the height h and the sum of its bases b1 and b2. Find the equation of joint variation if A = 48 in^3, h = 8 in., b1 = 5 in. and b2 = 7 in.

Practice If y varies jointly as x and z and y = 45 when x = 9 and z = 15, find y when x = 25 and z = 12 If y varies jointly as x and z and y = 45 when x = 9 and z = 15, find y when x = 25 and z = 12

Practice If y varies inversely as x and y = ¼ when x = 24, find y when x = ¾ If y varies inversely as x and y = ¼ when x = 24, find y when x = ¾ y = 8

Y U TRY! If m varies directly as w and m = -15 when w = 2.5, find m when w = 12.5 If m varies directly as w and m = -15 when w = 2.5, find m when w = 12.5 y = ? A: 75B:-25C: -75D: 25

Example The power P in watts of an electrical circuit varies jointly as the resistance R and the square of the current I. For a 600- watt microwave oven that draws a current of 5.0 amperes, the resistance is 24 ohms. The power P in watts of an electrical circuit varies jointly as the resistance R and the square of the current I. For a 600- watt microwave oven that draws a current of 5.0 amperes, the resistance is 24 ohms. What is the resistance of a 200-watt refrigerator that draws a current of 1.7 amperes? What is the resistance of a 200-watt refrigerator that draws a current of 1.7 amperes?

Y U Practice The LEM (Lunar Exploration Module) used by astronauts to explore the moon’s surface during the Apollo space missions weighs about 30,000 pounds on Earth. On the moon there is less gravity so it weighs less, meaning that less fuel is needed to lift off from the moon’s surface. The force of gravity on Earth is about 6 times as much as that on the moon. How much does the LEM weigh on the moon? The LEM (Lunar Exploration Module) used by astronauts to explore the moon’s surface during the Apollo space missions weighs about 30,000 pounds on Earth. On the moon there is less gravity so it weighs less, meaning that less fuel is needed to lift off from the moon’s surface. The force of gravity on Earth is about 6 times as much as that on the moon. How much does the LEM weigh on the moon? Enter the number pounds in your clicker!

Answer y=kx 30,000 30,000 = 6x x= 5,000 lbs