Answer
See below:
Work Step by Step
Step 1: Convert the inequality to an equation by replacing \[\le \] by = sign.
\[y=-\frac{1}{2}x+2\]
Step 2: Graph the equation using intercept form or slope-intercept form.
Make \[x=0\] to find y-intercept.
\[\begin{align}
& y=-\frac{1}{2}x+2 \\
& y=0+2 \\
& y=2
\end{align}\]
Make \[y=0\] to find x-intercept.
\[\begin{align}
& y=-\frac{1}{2}x+2 \\
& 0=-\frac{1}{2}x+2 \\
& x=4
\end{align}\]
The line passes through \[\left( 0,2 \right)\]and \[\left( 4,0 \right)\]. The line is solid, since the inequality contains \[\le \] symbol.
Step 3: Choose a test point. Let the origin \[\left( 0,0 \right)\] be the test point. Substitute it in the inequality.
\[\begin{align}
& y\le -\frac{1}{2}x+2 \\
& 0\le 2 \\
\end{align}\]
The statement is true. The graph contains the test point.
