Question

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

When $y=-8$, $x=8$. What is x when $y=-6$?

Short answer

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

The value of x when$y=-6$ is 6.

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 $y=-8,x=8$.

Therefore, substitute $-8$ for y and 8 for x in the equation $y=kx$to find the value of k.

$$\begin{gathered} y=kx \\ -8=k\left(8\right) \\ \frac{-8}{8}=k \\ -1=k \end{gathered}$$

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

Therefore, it is obtained that:

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

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

Step 2. Find the value of x when y=−6.

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

Find the value of x by substituting$-6$ for y in the equation $y=-x$.

$\begin{array}{c}y=-x\\ -6=-x\\ 6=x\end{array}$

Therefore, the value of x when$y=-6$ is 6.