# If y varies directly as x, and y=9 when x=4, how do you find y when x=16?

Jan 13, 2017

When $x = 16$, $y = 36$.

#### Explanation:

If $y$ varies directly as $x$, then if $y$ increases, $x$ increases, and if $y$ decreases, $x$ decreases. We can express this idea very succinctly in mathematics by writing $y = k x$. Where $k$ is a constant. Using this equation and substituting the initial values we have:
$y = k x$
$9 = k \cdot 4$
So $k = \frac{9}{4}$
Hence we can rewrite our general relationship more particularly in this case as $y = \frac{9}{4} x$.
Using the second set of values and our specific equation we get:
$y = \frac{9}{4} \cdot 16$
So $y = 36$