Answer
see graph
Work Step by Step
Changing the given inequality, $
2x+5y\lt-20
,$ to equality and then isolating $y$ result to
\begin{array}{l}\require{cancel}
2x+5y=-20
\\\\
5y=-2x-20
\\\\
y=-\dfrac{2}{5}x-\dfrac{20}{5}
\\\\
y=-\dfrac{2}{5}x-4
.\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}
2(0)+5(0)\lt-20
\\\\
0+0\lt-20
\\\\
0\lt-20
\text{ (FALSE)}
.\end{array}
Since the solution above ended with a $\text{
FALSE
}$ statement, then the test point is $\text{
NOT part
}$ of the solution set.