1. **State the problem:** We need to determine which inequality matches the given graph. 2. **Analyze the graph:** The line passes through the point $(2,4)$ with an open circle, meaning the point is not included in the solution set. The shaded region is above and to the left of the line. 3. **Check each inequality:** - Option a: $3x - 2y \geq 4$ - Option b: $3x - 4y \leq 2$ - Option c: $3x - 2y \leq 4$ 4. **Test the point $(2,4)$ in each inequality:** - For a: $3(2) - 2(4) = 6 - 8 = -2$ which is not $\geq 4$ (false) - For b: $3(2) - 4(4) = 6 - 16 = -10$ which is $\leq 2$ (true) - For c: $3(2) - 2(4) = 6 - 8 = -2$ which is not $\leq 4$ (true) 5. **Check the shading direction:** - The graph shows shading above and to the left of the line, which corresponds to $3x - 2y \geq 4$ (since the inequality is satisfied in that region). 6. **Open circle at $(2,4)$ means the inequality is strict (no equality), so $\geq$ or $\leq$ with equality included is not correct if the point is on the line but not included.** 7. **Since the line passes through $(2,4)$ but with an open circle, the inequality must be strict, but options a and c have $\geq$ or $\leq$ which include equality, so the open circle suggests the inequality is strict.** 8. **Given the shading and the line, the inequality that matches the graph is $3x - 2y \geq 4$ (option a).** **Final answer:** Option a: $3x - 2y \geq 4$