1. **State the problem:** We need to graph the inequality $$y \geq \frac{3}{2}x - 6$$ on a Cartesian coordinate plane. 2. **Understand the inequality:** The inequality means we want to shade the region where the value of $y$ is greater than or equal to the line $$y = \frac{3}{2}x - 6$$. 3. **Identify the line:** The line has slope $m = \frac{3}{2}$ and y-intercept $b = -6$. 4. **Plot the y-intercept:** Start by plotting the point $(0, -6)$ on the y-axis. 5. **Use the slope to find another point:** From $(0, -6)$, rise 3 units and run 2 units to the right to reach the point $(2, -3)$. 6. **Draw the boundary line:** Connect these points with a solid line because the inequality includes equality ($\geq$). 7. **Shade the region:** Since $y$ is greater than or equal to the line, shade the area above the line. This graph shows all points $(x,y)$ where $y$ is at least $$\frac{3}{2}x - 6$$. Final answer: The graph is a solid line with slope $\frac{3}{2}$ and y-intercept $-6$, shading the region above the line.