Answer
The graph is shown below.
Work Step by Step
The inequality is
$y\leq3x+2$
Step 1:- Replace the inequality symbol with $=$ and graph the linear equation.
$y=3x+2$
Now use the slope and the $y-$ intercept to graph.
The equation is in the form of $y=mx+b$.
Where, slope $m=\frac{3}{1}=\frac{Rise}{Run}$ and $y-$ intercept $=2$.
Therefore the first point is $A=(0,2)$
For the second point we move three unit up (rise) and one units right side (run).
The second point is $B=(1,5)$
There is equality sign therefore we draw a solid line through both points.
Step 2:- Choose a test point and plug into the inequality.
Let the test point $C=(1,1)$.
Plug the test point into inequality.
$\Rightarrow (1)\leq3(1)+2$
Simplify.
$\Rightarrow 1\leq3+2$
$\Rightarrow 1\leq5$
The statement is correct.
The solution set contains the test point.
Hence, the lower part of the line is the solution set.
