Find the x- and y-intercepts of the graph of 2, x, plus, 6, y, equals, 242x+6y=24. State each answer as an integer or an improper fraction in simplest form.
To find the x-intercept, we set $y=0$ and solve for $x$: \begin{align*}
242x+6(0)&=24\\
242x&=24\\
x&=\frac{24}{242}=\frac{12}{121}.
\end{align*} To find the $y$-intercept, we set $x=0$ and solve for $y$: \begin{align*}
242(0)+6y&=24\\
6y&=24\\
y&=4.
\end{align*} Thus, the $x$-intercept is $\boxed{\frac{12}{121}}$ and the $y$-intercept is $\boxed{4}$.