1. 3.8 Direct, Inverse, and Joint Variation
Objective: Solve problems involving direct, inverse, and joint variation.

2. y = kx Direct Variation: Ex.1)
y = kx
Ex.1)
Suppose y varies directly as x and y=45 when x = 2.5.
a.) Find the constant of variation and write an equation in the form y=kx^n
b.) Use the equation to find the value of y when x=4.

3. 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 feet.
a.) Write an equation of direct variation relating travel distance to time elapsed. Then graph the equation.
b.) Use the equation to find the distance traveled by the car in 8 minutes.
Ex.3)
If y varies directly as the square of x and y=30 when x=4, find x when y=270.

4. If y varies inversely as x and y=14 when x=3, find x when y=30.
Inverse Variation:
Ex. 4)
If y varies inversely as x and y=14 when x=3, find x when y=30.

5. Joint Variation:
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.