1. The problem asks to identify the correct graph for the inequality $y < \frac{1}{2}x - 4$. 2. The inequality is linear and in slope-intercept form $y < mx + b$ where $m = \frac{1}{2}$ and $b = -4$. 3. The boundary line is $y = \frac{1}{2}x - 4$. 4. Since the inequality is strictly less than ($<$), the boundary line should be dashed to indicate points on the line are not included. 5. The solution region is where $y$ is less than $\frac{1}{2}x - 4$, so the area below the line should be shaded. 6. Checking the graphs: - Graph A: line is dashed but shaded region is above the line (incorrect). - Graph B: line is solid and shaded below (line should be dashed, so incorrect). - Graph C and D: lines have wrong slope and intercept (incorrect). 7. The correct graph must have a dashed line $y = \frac{1}{2}x - 4$ and shading below the line. 8. None of the given graphs exactly match this, but Graph A has the correct dashed line and correct line equation, only shading is wrong. 9. Since the problem asks which is correct, the best match is Graph A except shading is above instead of below. 10. Therefore, the correct solution is a dashed line $y = \frac{1}{2}x - 4$ with shading below the line. Final answer: The correct graph should have a dashed line $y = \frac{1}{2}x - 4$ and shading below the line, which none of the given graphs perfectly show, but Graph A has the correct line and dashed style.