Answer
see graph
Work Step by Step
Changing the given inequality, $
\dfrac{1}{2}x-y\lt2
,$ to equality and then isolating $y$ result to
\begin{array}{l}\require{cancel}
\dfrac{1}{2}x-y=2
\\\\
-y=-\dfrac{1}{2}x+2
\\\\
y=\dfrac{1}{2}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}
\dfrac{1}{2}(0)-0\lt2
\\\\
0\lt2
\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.