Algebra: A Combined Approach (4th Edition)

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)