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**3.8 Direct, Inverse and Joint Variation**

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**Direct Variation y = kxn, n>0 k is the constant of variation**

The relationship between braking distance and car speed. As the speed of the car increases, the braking distance also increases at a constant rate

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**Ex 1 suppose y varies directly as x and y = 45 when x = 5/2**

Find the constant of variation and write an equation Use the equation to find the value of y when x = 4

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Ex 2 When an object such as a car is accelerating, twice the distance d it travels varies directly with the square of the time t elapsed. One car accelerating for 4 minutes travels 1440 ft. Write an equation. Find the distance traveled in 8 minutes.

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Ex 3 If y varies directly as the square of x and y = 30 and x = 4, find x when y = 270.

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**Inverse Variation (Inversely proportional)**

As one value increases the other decreases. When you travel to a higher elevation above Earth’s surface, the air temperature decreases.

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**Can use proportions to solve inverse variation:**

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**Ex 4 If y varies inversely as x and y = 14 when x =3, find x when y = 30.**

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**Joint Variation – when one quantity varies directly as the product of two or more other quantities.**

y = kxnzn where x and z cannot = 0 and n > 0

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Ex 5 In Physics, the work W done in charging a capacitor varies jointly as the charge q and the voltage V. Find the equation of joint variation if a capacitor with a charge of coulomb and a voltage of 100 volts performs 0.20 joule of work.

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What You Will Learn Recognize and solve direct and joint variation problems Recognize and solve inverse variation problems.

What You Will Learn Recognize and solve direct and joint variation problems Recognize and solve inverse variation problems.

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