Answer
\begin{align*}
\text{$x$-intercept: }&
(9, 0)
\\
\text{$y$-intercept: }&
(0, -3)
\end{align*}
Work Step by Step
To find the $x$-intercept of the given equation, $
x-3y=9
,$ substitute $y=0$ and then solve for $x.$ That is,
\begin{align*}
x-3(0)&=9
\\
x-0&=9
\\
x&=9
\end{align*}
To find the $y$-intercept of the given equation, substitute $x=0$ and then solve for $y.$ That is,
\begin{align*}
0-3y&=9
\\
-3y&=9
\\\\
\dfrac{-3y}{-3}&=\dfrac{9}{-3}
\\\\
y&=-3
\end{align*}
Hence, the intercepts of the given equation are
\begin{align*}
\text{$x$-intercept: }&
(9, 0)
\\
\text{$y$-intercept: }&
(0, -3)
\end{align*}
