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Math 1310 Class Notes – Section 3.3, Page 1 of 7
Math 1310
Section 3.3
Variation (Proportions)
You’ll be asked to solve some problems involving
functions using
variation.
We’ll consider three types
of variation.
•
Variation formulas
Direct variation
:
We say
y
varies directly as
x
, or
y
is directly proportional to
x
, if
,
y
kx
=
where
k
is a
constant
( 29
0 .
k
≠
Inverse variation
:
We say
y
varies inversely as
x
, or
y
is inversely proportional to
x
, if
,
k
y
x
=
where
k
is a
constant
( 29
0 .
k
≠
Joint variation
:
We way
y
varies jointly as
x
and
z
,
or
y
is jointly proportional to
x
and
z
, if
,
y
kxz
=
where
k
is a constant
( 29
0 .
k
≠
In each instance above,
k
is called the constant of
proportionality.
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You’ll be asked to find one (or more) of three things:
•
a formula that corresponds to a given statement
•
the constant of proportionality,
k
•
a value for one variable, given other values
Example 1:
Suppose
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 Summer '08
 MARKS
 Direct Variation, Inverse Variation, Formulas

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