Answer
The graph is shown below.
Work Step by Step
The given equation of the line is
$\Rightarrow 2x-3y=12$
Plug $y=0$ for the $x−$intercept.
$\Rightarrow 2x-3(0)=12$
Simplify.
$\Rightarrow 2x=12$
Divide both sides by $2$.
$\Rightarrow \frac{2x}{2}=\frac{12}{2}$
Simplify.
$\Rightarrow x=6$
The $x−$intercept is 6, so the line passes through (6,0).
Plug x=0 for the y−intercept.
$\Rightarrow 2(0)-3y=12$
Simplify.
$\Rightarrow -3y=12$
Divide both sides by $-3$.
$\Rightarrow \frac{-3y}{-3}=\frac{12}{-3}$
Simplify.
$\Rightarrow y=-4$
The $y−$intercept is $-4$, so the line passes through $(0,-4)$.
Checkpoint plug $x=3$.
$\Rightarrow 2(3)-3y=12$
Simplify.
$\Rightarrow 6-3y=12$
Subtract $6$ from both sides.
$\Rightarrow 6-3y-6=12-6$
Simplify.
$\Rightarrow -3y=6$
Divide both sides by $-3$.
$\Rightarrow \frac{-3y}{-3}=\frac{6}{-3}$
Simplify.
$\Rightarrow y=-2$
The checkpoint is (3,-2).
Plot the three points determines above. Draw a straight line through the points $(6,0)$ and $(0,-4)$. We notice that the checkpoint $(3,-2)$ also belongs to the line, therefore our graph is correct.