Question

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

If$y=4$when $x=-4$, find y when $x=7$.

Short answer

The direct variation equation that relates x and y is $y=-x$.

The value of y when$x=7$ is $-7$.

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 $x=-4,y=4$.

Therefore, substitute $-4$ for x and 4 for y in the equation $y=kx$ to find the value of k.

$\begin{array}{c}y=kx\\ 4=k\left(-4\right)\\ \frac{4}{-4}=k\\ -1=k\end{array}$

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

Therefore, it is obtained that:

$\begin{array}{c}y=kx\\ y=\left(-1\right)x\\ y=-x\end{array}$

Therefore, the direct variation equation that relates x and y is $y=-x$.

Step 2. Find the value of y when x=7.

The direct variation equation that relates x and y is $y=-x$.

Find the value of y by substituting 7 for x in the equation $y=-x$.

$$\begin{gathered} y=-x \\ =-7 \end{gathered}$$

Therefore, the value of y when$x=7$ is $-7$.