Answer
The graph is shown below.
Work Step by Step
The inequality is
$x-3y\leq6$
Step 1:- Replace the inequality symbol with $=$ and graph the linear equation.
$x-3y=6$
Plug $y=0$ for the $x−$intercept.
$\Rightarrow x-3(0)=6$
Simplify.
$\Rightarrow x=6$
The $x−$intercept is $6$, so the line passes through $A=(6,0)$.
Plug $x=0$ for the $y−$intercept.
$\Rightarrow (0)-3y=6$
Simplify.
$\Rightarrow -3y=6$
Multiply 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 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.
$\Rightarrow 0-3(0)\leq6$
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.
