#### Answer

$x\text{-intercept: }
\left( 8,0 \right)
\\y\text{-intercept: }
(0,-2)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the definition of intercepts to find the $x$- and $y$-intercepts of the given equation, $
x-4y=8
.$ Then plot the points corresponding to the intercepts and connect these with a line to get the graph.
$\bf{\text{Solution Details:}}$
The $x$-intercept is the value of $x$ when $y=0.$ Substituting $y=0$ in the given equation, then
\begin{array}{l}\require{cancel}
x-4y=8
\\\\
x-4(0)=8
\\\\
x-0=8
\\\\
x=8
.\end{array}
Hence, the $x$-intercept is $
\left( 8,0 \right)
.$
The $y$-intercept is the value of $y$ when $x=0.$ Substituting $x=0$ in the given equation, then
\begin{array}{l}\require{cancel}
x-4y=8
\\\\
0-4y=8
\\\\
-4y=8
\\\\
y=\dfrac{8}{-4}
\\\\
y=-2
.\end{array}
Hence, the $y$-intercept is $
(0,-2)
.$
Connecting the following intercepts,
\begin{array}{l}\require{cancel}
x\text{-intercept: }
\left( 8,0 \right)
\\y\text{-intercept: }
(0,-2)
,\end{array}
gives the graph of the given equation.