Question

If f(x) varies directly with x, and f(x) = 8 when x = 6, write the direct linear variation equation.

Answer 1

f(6)=8

Answer 2

\(\bf \begin{array}{cccllll}
\textit{something }&\textit{varies directly to }&\textit{something else}\\ \quad \\
\textit{something }&={\color{red}{ \textit{some value }}}&\textit{something else}\\ \quad \\
y&={\color{red}{ n}}&x&\implies y={\color{red}{ n}}x
\end{array}\\ \quad \\
f(x)=y = 8\qquad x=6\implies 8={\color{red}{ n}}(6)\qquad \textit{solve for "n"}\)

once you find "n", or the "constant of variation", plug it back in the original equation