Question

If y varies directly as x, and y = 15 as x = -3, find y for the x-value of 6

Answer 1

\(\bf \begin{array}{cccllll}
\textit{something }&\textit{varies directly to }&\textit{something else}\\ \quad \\
\textit{something }&={\color{red}{ \textit{some value }}}&\textit{something else}\\ \quad \\
y&={\color{red}{ n}}&x&\implies y={\color{red}{ n}}x
\end{array}\\ \quad \\
y = 15 \qquad x = -3\implies 15={\color{red}{ n}}(-3)\)

solve for "n", or "constant of variation"

once you find "n", plug in its value in the original equation
to find "y" when x = 6, well, just set "x" to 6 and solve for "y"