Section 2.5
Variation
Variation describes how one quantity varies (changes) in a proportional relationship with another
quantity.
Quantities my vary directly, inversely, jointly
or with combined variation.
k = the constant of variation or proportionality.
(n may equal 1,
x = x
1
.)
In most variation questions, x and y are known for one case.
Find k, then write a formula to use for
all cases.
Direct Variation – both quantities or up or both quantities go down.
For example:
As the number of miles driven increases, the more fuel is used.
Another example:
As the speed of a car increases, stopping distance required increases.
Direct Variation Formula
If y varies directly with x
n
, then
y = kx
n
.
Suppose y varies directly as the cube of x.
If y = 4 when x = 2, what is the value of y when x = 4?
You may also use a proportion to solve direct variation questions.
Indirect or Inverse Variation
inverse (or indirect) variation

as one quantity increases, the other decreases
For example:
As distance between objects increases the force of gravity between decreases.
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 Fall '08
 staff
 Algebra, Direct Variation, Inverse Variation, Mass, variation

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