1. **State the problem:** Sketch the graph of the linear inequality $y \geq -3x + 4$. 2. **Formula and rules:** The boundary line is given by the equation $y = -3x + 4$. For inequalities of the form $y \geq mx + b$, the graph includes the line and the region above it. 3. **Plot the boundary line:** The line passes through the y-intercept $(0,4)$ and has slope $-3$, meaning it goes down 3 units for every 1 unit right. 4. **Shade the region:** Since the inequality is $y \geq -3x + 4$, shade the region above the line. 5. **Summary:** The graph consists of the line $y = -3x + 4$ (solid line because of \geq) and the shaded region above it. Final answer: The graph of $y \geq -3x + 4$ is the solid line $y = -3x + 4$ with shading above the line.