Answer
The graph is shown below.
Work Step by Step
The inequality is
$y\lt-\frac{1}{3}x$
Step 1:- Replace the inequality symbol with $=$ and graph the linear equation.
$y=-\frac{1}{3}x$
Now use the slope and the $y-$ intercept to graph.
The equation in the form of $y=mx+b$ is.
$y=-\frac{1}{3}x+0$
Where, slope $m=\frac{-1}{3}=\frac{Rise}{Run}$ and $y-$ intercept $=0$.
Therefore the first point is $A=(0,0)$
For the second point we move one unit down (rise) and three units right side (run).
The second point is $B=(3,-1)$
There is no equality sign therefore we draw a dashed 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.
$\Rightarrow (1)\lt-\frac{1}{3}(1)$
Simplify.
$\Rightarrow 1\lt-\frac{1}{3}$
The statement is not correct.
The solution set does not contain the test point.
Hence, the lower part of the line is the solution set.
