1. **State the problem:** We need to graph the inequality $y \geq \frac{3}{4}x - 4$ on the coordinate plane. 2. **Understand the inequality:** The inequality $y \geq \frac{3}{4}x - 4$ means that $y$ is greater than or equal to the line $y = \frac{3}{4}x - 4$. 3. **Graph the boundary line:** First, graph the line $y = \frac{3}{4}x - 4$. This line has a slope of $\frac{3}{4}$ and a y-intercept at $-4$. 4. **Plot the y-intercept:** Start at the point $(0, -4)$ on the y-axis. 5. **Use the slope to find another point:** From $(0, -4)$, move up 3 units and right 4 units to reach the point $(4, -1)$. 6. **Draw the boundary line:** Connect these points with a solid line because the inequality includes equality ($\geq$). 7. **Shade the solution region:** Since $y$ is greater than or equal to the line, shade the region above the line. 8. **Check a test point:** For example, at $(0,0)$, check if $0 \geq \frac{3}{4}(0) - 4$ which simplifies to $0 \geq -4$, true, so shade above the line. **Final answer:** The graph is the solid line $y = \frac{3}{4}x - 4$ with the region above it shaded, representing all points where $y \geq \frac{3}{4}x - 4$.