[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \textit{\underline{m} varies directly with the amount of gallons}\implies \stackrel{months}{m}=k\stackrel{gallons}{g}
\\\\\\
\textit{we also know that }
\begin{cases}
m=1\frac{1}{3}\\
\qquad \frac{4}{3}\\
g=1
\end{cases}\implies \cfrac{4}{3}=k1\implies \cfrac{4}{3}=k
\\\\\\
\boxed{m=\cfrac{4}{3}g}\\\\
-------------------------------\\\\
\textit{what's \underline{m} when g=7?}\qquad m=\cfrac{4}{3}\cdot 7\implies m=\cfrac{28}{3}\implies m=9\frac{1}{3}[/tex]
