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GETTING BIGGER? GETTING SMALLER?
(Direct and Inverse Variation)
Jump right to the exercises!
Remember that bigger means farther away from zero and
smaller means closer to zero .
Suppose that y=2x .
When x gets bigger, y gets bigger.
When y gets bigger, x gets bigger.
In this type of relationship, x and y "follow each other" in size:
when one gets bigger, so does the other. When one gets smaller, so does the other.
This kind of relationship between two variables is called direct variation :
if there is a nonzero number k for which
y=kx ,
then we say that " y varies directly as x ".
Now suppose that y=2x .
When x gets bigger, y gets smaller.
When x gets smaller, y gets bigger.
In this type of relationship, x and y have sizes that go
in different directions:
when one gets bigger, the other gets smaller. When one gets smaller, the other gets bigger.
This kind of relationship between two variables is called inverse variation :
if there is a nonzero number k for which
y=kx ,
then we say that " y varies inversely as x ".
EXAMPLES:
Question: Consider the formula
P V
=
nRT
.
As T gets bigger, what happens to V ?
(Assume all other variables are held constant.)
Solution: V gets bigger
There is a direct relationship between T and V .
As T gets bigger, so does V .
Intuition: Both variables are "upstairs" on opposite sides of the equation.
Question: Consider the formula
P
=
nRT
V
.
As P gets bigger, what happens to V ?
(Assume all other variables are held constant.)
Solution: V gets smaller
There is an inverse relationship between P and V .
As P gets bigger, V gets smaller.
Intuition: One variable is "upstairs" and the other "downstairs" on opposite sides of the equation.
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