Answer
The graph is shown below.
Work Step by Step
The inequality is
$y\gt\frac{1}{4}x$
Step 1:- Replace the inequality symbol with $=$ and graph the linear equation.
$y=\frac{1}{4}x$
Now use the slope and the $y-$ intercept to graph.
The equation in the form of $y=mx+b$ is
$\Rightarrow y=\frac{1}{4}x+0$
Where, slope $m=\frac{1}{4}=\frac{Rise}{Run}$ and $y-$ intercept $=0$.
Therefore the first point is $A=(0,0)$
For the second point we move one unit up (rise) and four units right side (run).
The second point is $B=(4,1)$
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.
$\Rightarrow (1)\gt\frac{1}{4}(1)$
Simplify.
$\Rightarrow 1\gt\frac{1}{4}$
The statement is correct.
The solution set contains the test point.
Hence, the upper part of the line is the solution set.
