Answer
See below:
Work Step by Step
Step 1: Convert the inequality to an equation by replacing < by = sign.
\[x-3y=6\]
Step 2: Graph the equation using intercept form or slope-intercept form.
Make \[x=0\] to find the y-intercept,
\[\begin{align}
& x-3y=6 \\
& 0-3y=6 \\
& y=-2
\end{align}\]
Make \[y=0\] to find x-intercept,
\[\begin{align}
& x-3y=6 \\
& x-0=6 \\
& x=6
\end{align}\]
The line passes through \[\left( 6,0 \right)\]and \[\left( 0,-2 \right)\]. The line is solid since the inequality contains the \[\le \]symbol.
Step 3: Choose a test point. The origin \[\left( 0,0 \right)\]be the test point. Substituting in the inequality,
\[\begin{align}
& x-3y\le 6 \\
& 0\le 6
\end{align}\]
The statement is true. The graph contains the test point.
