[tex]\bf \begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
\\
&& y={{ k }}x
\end{array}\\\\
-----------------------------\\\\
[/tex]
[tex]\bf \textit{now, we also know }\qquad
\begin{cases}
y=400\\
x=r\\
---\\
y=r\\
x=4
\end{cases}\implies
\begin{cases}
400=kr\\
r=k4\\
----------\\
now\\
400=kr\implies \frac{400}{k}=\boxed{r}\\\\
thus\\\\
r=k4\implies \boxed{\frac{400}{k}}=4k
\end{cases}
\\\\\\
400=4k^2\implies \cfrac{400}{4}=k^2\implies 100=k^2\implies \sqrt{100}=k
\\\\\\
10=k\impliedby \textit{constant of variation}[/tex]
