1. **State the problem:** We need to graph the inequality $y > \frac{1}{2}x - 6$. 2. **Understand the boundary line:** The boundary line is given by the equation $y = \frac{1}{2}x - 6$. 3. **Plot points on the boundary line:** - When $x=0$, $y = \frac{1}{2}(0) - 6 = -6$. - When $x=2$, $y = \frac{1}{2}(2) - 6 = 1 - 6 = -5$. - When $x=4$, $y = \frac{1}{2}(4) - 6 = 2 - 6 = -4$. 4. **Draw the boundary line:** Since the inequality is strict ($>$), the boundary line should be dotted (not solid). 5. **Shade the region:** The inequality $y > \frac{1}{2}x - 6$ means we shade the region above the boundary line. 6. **Summary:** - Plot the dotted line $y = \frac{1}{2}x - 6$ using points like $(0,-6)$, $(2,-5)$, and $(4,-4)$. - Shade the area above this line. This completes the graphing of the inequality.