Answer
see graph
Work Step by Step
Changing the given inequality, $
3x+y\gt4
,$ to equality and then isolating $y$ result to
\begin{array}{l}\require{cancel}
3x+y=4
\\\\
y=-3x+4
.\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}
3(0)+0\gt4
\\\\
0\gt4
\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.