Bigger means
farther away from zero
and
smaller means
closer to zero.
(This is discussed in more detail in a future section.)
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 $\,y = \frac{2}{x}\,$.
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 $\displaystyle \,y = \frac{k}{x}\,$,
then we say that
‘$\,y\,$ varies inversely as $\,x\,$’.
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.However, you can check to see if your answer is correct. 
PROBLEM TYPES:
