# If y varies directly as the cube of x, what is the value of y in the ordered pairs (4,16) and (2,y)?

Jul 3, 2016

$y = 2$

#### Explanation:

We can interpret "y varies directly as the cube of x" as following formula:

$y = k {x}^{3}$, where k = some constant that we need to find.

We are given one order pair $\left(4 , 16\right)$ from which we can find the value of k.

So, $16 = k \cdot {4}^{3}$

$16 = k \cdot 64$

$k = \frac{16}{64} = \frac{1}{4}$

Now, we can use our original formula $y = k {x}^{3}$ and pluging $\frac{1}{4}$ for $k$. That would give us $y = \frac{1}{4} {x}^{3}$.

To find $y$ in $\left(2 , y\right)$, we just need to plugin 2 for $x$.

$y = \frac{1}{4} \cdot {2}^{3}$

$y = \frac{1}{4} \cdot 8$

$y = 2$