Q37. - Algebra 1

Question

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

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

Step-by-Step Solution

Answer

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

The value of y when $x=7$ is $-7$.

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 $-7$.