Question

Suppose yvaries directly as x. Write a direct variation equation that relates x and y. Then solve.

If$y=15$ when $x=2$, find y when $x=8$.

Short answer

The direct variation equation that relates x and y is $y=\frac{15}{2}x$.

The value of y when$x=8$ is 60.

Step-by-step solution

Step 1. Write a direct variation equation that relates x and y.

It is given that y varies directly as x.

Therefore it implies that $y\alpha x$.

Therefore, it is obtained that:

$\begin{array}{l}y\alpha x\\ y=kx\end{array}$

Where k is constant of proportionality.

It is given that when $x=2$, $y=15$.

Therefore, substitute 2 for x and 15 for y in the equation $y=kx$ to find the value of k.

$\begin{array}{c}y=kx\\ 15=k\left(2\right)\\ \frac{15}{2}=k\end{array}$

Substitute the value of k in the equation $y=kx$.

Therefore, it is obtained that:

$\begin{array}{c}y=kx\\ y=\frac{15}{2}x\end{array}$

Therefore, the direct variation equation that relates x and y is $y=\frac{15}{2}x$.

Step 2. Find the value of y when x=8.

The direct variation equation that relates x and y is $y=\frac{15}{2}x$.

Find the value of y by substituting 8 for x in the equation $y=\frac{15}{2}x$.

$\begin{array}{c}y=\frac{15}{2}x\\ y=\frac{15}{2}\left(8\right)\\ y=15\left(4\right)\\ y=60\end{array}$

Therefore, the value of y when$x=8$ is 60.