Answer
see graph
Work Step by Step
Changing the given inequality, $
5x+3y\gt-15
,$ to equality and then isolating $y$ result to
\begin{array}{l}\require{cancel}
5x+3y=-15
\\\\
3y=-5x-15
\\\\
y=-\dfrac{5}{3}x-\dfrac{15}{3}
\\\\
y=-\dfrac{5}{3}x-5
.\end{array}
Use the table of values below to graph this line.
Since the inequality used is "$
\gt
$", use broken lines.
Using the test point $(
0,0
)$, then
\begin{array}{l}\require{cancel}
5x+3y\gt-15
\\\\
5(0)+3(0)\gt-15
\\\\
0+0\gt-15
\\\\
0\gt-15
\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.