Answer
Refer to the image below for the graph.
Work Step by Step
To graph the given inequality, perform the following steps:
(1) Graph the boundary line $y=\frac{1}{2}x-4$ using a solid line since it involves $\ge$.
(refer to the image below for the graph)
(2) Use the test point $(0, 0)$. Substitute the x and y values of this point into the given inequality to obtain:
\begin{array}{ccc}
\\&0&\ge &\frac{1}{2}(0)-4
\\&0 &\ge &0-4
\\&0 &\ge &-4
\end{array}
The statement is true.
(3) The resulting statement in step (2) is true.
This means that the solution set is the region that contains the test point $(0, 0)$.
To complete the graph, shade the region that contains $(0, 0)$.
(refer to the attached image in the answer part above for the graph)