Answer
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow y\leq-\frac{3}{2}x+3$.
Step 1:- Replace the inequality symbol and graph the linear equation.
$\Rightarrow y=-\frac{3}{2}x+3$.
The slope is $=\frac{-3}{2}=\frac{rise}{run}$. The $y-$ intercept is $=3$.
The line passes through $A=\left(0,3 \right )$.
Step 2:- Choose a test point.
Let the test point be $B=(0,0)$.
Substitute the test point into the inequality.
$\Rightarrow (0)\leq-\frac{3}{2}(0)+3$.
Simplify.
$\Rightarrow 0\leq3$.
The statement is correct. Shade the half-plane containing the test point.
