Answer
Direct Variation
$y = \frac{x}{2}$
Work Step by Step
A quick way to recognize direct and inverse variation is to ask, "as x goes up in value, what does y do?" If y goes up, then it is a direct variation. If y goes down, then it is an inverse variation.
In this case, as x goes up, y also goes up, meaning it is a direct variation.
Another way is to check each ratio of \frac{y}{x}. If the result is the same answer for each, then it is a direct variation and we have found our k value.
$\frac{1}{2} =\frac{1}{2} $
$\frac{2.5}{5} = \frac{1}{2} $
$\frac{4}{8} = \frac{1}{2} $
Again, we see that it is a direct variation and $k=\frac{1}{2}$
Therefore, the equation for this direct variation is:
$y=\frac{1}{2}x$ or $y=\frac{x}{2}$
