Answer
see graph
Work Step by Step
Changing the given inequality, $
2x+6y\le12
,$ to equality and then isolating $y$ result to
\begin{array}{l}\require{cancel}
2x+6y=12
\\\\
6y=-2x+12
\\\\
y=-\dfrac{2}{6}x+\dfrac{12}{6}
\\\\
y=-\dfrac{1}{3}x+2
.\end{array}
Use the table of values below to graph this line.
Since the inequality used is "$
\le
$", use solid lines.
Using the test point $(
0,0
)$, then
\begin{array}{l}\require{cancel}
2(0)+6(0)\le12
\\\\
0+0\le12
\\\\
0\le12
\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.