Answer
The graph is shown below.
Work Step by Step
The inequality is
$3x-y\leq6$
Step 1:- Replace the inequality symbol with $=$ and graph the linear equation.
$3x-y=6$
Plug $y=0$ for the $x−$intercept.
$\Rightarrow 3x-0=6$
Simplify.
$\Rightarrow 3x=6$
Divide both sides by $3$.
$\Rightarrow \frac{3x}{3}=\frac{6}{3}$
Simplify.
$\Rightarrow x=2$
The $x−$intercept is $2$, so the line passes through $A=(2,0)$.
Plug $x=0$ for the $y−$intercept.
$\Rightarrow 3(0)-y=6$
Simplify.
$\Rightarrow -y=6$
Multiply both sides by $-1$.
$\Rightarrow -1(-y)=-1(6)$
Simplify.
$\Rightarrow y=-6$
The $y−$intercept is $-6$, so the line passes through $B=(0,-6)$.
Draw a straight line through these intercept points.
Step 2:- Choose a test point and plug into the inequality.
Let the test point $C=(0,0)$.
Plug the test point into inequality.
$\Rightarrow 3(0)-(0)\leq6$
Simplify.
$\Rightarrow 0\leq6$
The statement is correct.
The solution set contains the test point.
Hence, the upper part of the line is the solution set.
