Answer
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 2x-3y\lt-6$.
Step 1:- Replace the inequality symbol by $=$ and graph the linear equation.
$\Rightarrow 2x-3y=-6$.
Plug $y=0$ into the linear equation.
$\Rightarrow 2x-3(0)=-6$
$\Rightarrow 2x=-6$
Divide both sides by $2$.
$\Rightarrow \frac{2x}{2}=\frac{-6}{2}$
Simplify.
$\Rightarrow x=-3$
The $x-$ intercept is $-3$, so the line passes through $A=(-3,0)$.
Plug $x=0$ into the linear equation.
$\Rightarrow 2(0)-3y=-6$
$\Rightarrow -3y=-6$
Divide both sides by $-3$.
$\Rightarrow \frac{-3y}{-3}=\frac{-6}{-3}$
Simplify.
$\Rightarrow y=2$
The $y-$ intercept is $2$, so the line passes through $B=(0,2)$.
Draw a dashed line through these two points because equality is not included.
Step 2:- Choose a test point.
Let the test point be $C=(0,0)$.
Substitute the test point into given inequality.
$\Rightarrow 2(0)-3(0)\lt-6$.
Simplify.
$\Rightarrow 0\lt-6$. The statement is false.
Shade the half-plane not containing the test point.
