Answer
see graph
Work Step by Step
Changing the given inequality, $
x-3y\lt0
,$ to equality and then isolating $y$ result to
\begin{array}{l}\require{cancel}
x-3y=0
\\\\
-3y=-x
\\\\
y=\dfrac{-1}{-3}x
\\\\
y=\dfrac{1}{3}x
.\end{array}
Use the table of values below to graph this line.
Since the inequality used is "$
\lt
$", use a broken line.
Using the test point $(
-2,2
)$, then
\begin{array}{l}\require{cancel}
-2-3(2)\lt0
\\\\
-2-6\lt0
\\\\
-8\lt0
\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.