Answer
see graph
Work Step by Step
Changing the given inequality, $
x+2y\gt0
,$ to equality and then isolating $y$ result to
\begin{array}{l}\require{cancel}
x+2y=0
\\\\
2y=-x
\\\\
y=-\dfrac{1}{2}x
.\end{array}
Use the table of values below to graph this line.
Since the inequality used is "$
\gt
$", use a broken line.
Using the test point $(
0,2
)$, then
\begin{array}{l}\require{cancel}
0+2(2)\gt0
\\\\
0+4\gt0
\\\\
4\gt0
\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.