Question

If y=6 when x=-3 find x when y= 24y varies directly with x

Answer 1

Since y varies directly with x then

`\begin{gathered} (y)/(x)=k \\ \text{Where k is the constant of proportionality} \end{gathered}`

So,

`\begin{gathered} (y)/(x)=(6)/(-3) \\ (y)/(x)=-2 \end{gathered}`

Then, -2 is the constant of proportionality. So that,

`\begin{gathered} (y)/(x)=-2 \\ (24)/(x)=-2 \\ \text{Solving for x you have} \\ (24)/(x)\cdot x=-2\cdot x \\ 24=-2x \\ (24)/(-2)=(-2x)/(-2) \\ -12=x \end{gathered}`

Therefore, if y=6 when x=-3, then x=-12 when y=4.