Answer
see graph
Work Step by Step
Changing the given inequality, $
x-4y\lt8
,$ to equality and then isolating $y$ result to
\begin{array}{l}\require{cancel}
x-4y=8
\\\\
-4y=-x+8
\\\\
y=\dfrac{-1}{-4}x+\dfrac{8}{-4}
\\\\
y=\dfrac{1}{4}x-2
.\end{array}
Use the table of values below to graph this line.
Since the inequality used is "$
\lt
$", use broken lines.
Using the test point $(
0,0
)$, then
\begin{array}{l}\require{cancel}
0-4(0)\lt8
\\\\
0-0\lt8
\\\\
0\lt8
\text{ (TRUE)}
.\end{array}
Since the solution above ended with a $\text{
TRUE
}$ statement, then the test point is $\text{
part
}$ of the solution set.