1. The problem is to graph the inequality $y \geq \frac{4}{3}x - 8$ on a Cartesian coordinate system. 2. The boundary line is given by the equation $y = \frac{4}{3}x - 8$. This line has a slope of $\frac{4}{3}$ and a y-intercept of $-8$. 3. To graph the line, start at the point $(0, -8)$ on the y-axis. 4. From the y-intercept, use the slope $\frac{4}{3}$ to find another point: move up 4 units and right 3 units to reach the point $(3, -4)$. 5. Draw a solid line through these points because the inequality includes equality ($\geq$). 6. The inequality $y \geq \frac{4}{3}x - 8$ means the solution region is all points on or above the line. 7. Shade the region above the line to represent all points where $y$ is greater than or equal to $\frac{4}{3}x - 8$. This completes the graphing of the inequality.