Question

if y varies directly as x and y=14 as x=7, find y for the x-value of 10

Answer 1

\(\bf \begin{array}{cccllll}
\textit{something }&\textit{varies directly to }&\textit{something else}\\ \quad \\
\textit{something }&={\color{red}{ \textit{some value }}}&\textit{something else}\\ \quad \\
y&={\color{red}{ n}}&x&\implies y={\color{red}{ n}}x
\end{array}\\ \quad \\
y=14\qquad x=7\implies 14={\color{red}{ n}}(7)\qquad \textit{solve for "n"}\)

once you have "n" value, or the "constant of variation"
plug it in the original equation

then set x = 10 to find what "y" would be

Answer 2

what is an appropriate direct variation equation if y=8 when x=2