Outline Sec. 2-1Outline Sec. 2-1

Direct VariationDirect VariationAlgebra II CPAlgebra II CP

Mrs. SweetMrs. Sweet

Some states offer refunds for returning aluminum cans. New York offers 5¢ for each can returned. If r represents the refund and c the number of cans returned write an equation to show this relationship.

What happens if you double the number of cans returned?

What happens if you triple the number of cans returned?

r = 5c

The refund increases.

The refund increases.

This is an example of variation

r varies as c directly

direct

The formula for the area of a circle is

Let r = 5cm.

Find the Area of the circle:

Let r = 10 cm.

Find the Area of the circle:

2A r

25A

100A

As the radius doubles what happens to the area?

It quadruples.

Since the Area increases when the radius increases this is an example of

direct -variation

Definition:

A function is a function with a formula of the form:

direct variation

ny kx with 0k and 0n

k is called the of variation constant

Examples • 1) The weight P of an object on another

planet varies directly with its weight on earth E.

• a) Write an equation relating P and E.

• b) Identify the dependent and independent variables.

P=kE

2) The cost c of gas for a car varies directly as the amount of gas g purchased.

a) Write an equation relating c and g.

3) The price of breakfast cereal varies directly as the number of boxes of cereal purchased.

a) Write an equation relating price and the number of boxes purchased.

4) The volume of a sphere varies directly as the cube of its radius.

Solving Direct Variation Problems:

1) Find the constant of variation if y varies directly as x, and y = 32 when x = 0.2.

Find y when x = 5.

2) The quantity of ingredients for the crust and toppings of a pizza, and therefore the price, is proportional to its area, not its linear dimensions. So, the quantity of ingredients is proportional to the square of its radius. Suppose that a pizza 12 inches in diameter costs $7.00. If the price of pizza varies directly as the square of its radius, what would a pizza 15 inches in diameter cost?

y varies directly as the square of x.

Find the constant of variation when x = -8 and y =588

Find y, when x = 10

Algorithm for using variation functions to predict values:

1) Write an that describes the function.

2) Find the of variation.

3) the variation function using the constant of variation.

4) the function for the desired value of the independent variable.

equation

constant

Rewrite

Evaluate