Transcript Outline Sec. 2-1

Outline Sec. 2-1
Direct Variation
Algebra II CP
Mrs. 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.
r = 5c
What happens if you double the number of cans returned?
The refund increases.
What happens if you triple the number of cans returned?
The refund increases.
This is an example of
r varies
direct
directly
variation
as c
The formula for the area of a circle is
A r
2
Let r = 5cm.
Find the Area of the circle:
A  25
Let r = 10 cm.
Find the Area of the circle:
A  100
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:
direct variation
A
function with a formula of the form:
y  kx
n
k is called the
with
k 0
and
function is a
n0
constant
of variation
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.
P=kE
• b) Identify the dependent and
independent variables.
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:
equation
1) Write an
describes the function.
2) Find the
3)
4)
constant
that
of variation.
Rewrite
the variation function
using the constant of variation.
Evaluate
the function for the
desired value of the independent variable.