1. The problem is to find which number line model represents the expression $3 \frac{1}{2} + (-6)$. 2. First, convert the mixed number to an improper fraction or decimal: $3 \frac{1}{2} = 3.5$. 3. The expression becomes $3.5 + (-6)$, which means starting at 3.5 on the number line and moving 6 units to the left (because of the negative sign). 4. Calculate the result: $$3.5 + (-6) = 3.5 - 6 = -2.5.$$ 5. On the number line, this means starting at 3.5, moving left past 0 to -2.5. 6. Now, analyze the graphs: - Graph A: First arrow goes left from -2 to -4 (moving left), second arrow goes right from 2 to 4. This does not start at 3.5. - Graph B: First arrow goes right from 2 to 4, second arrow goes right from 4 to 10. This shows movement to the right, not left. - Graph C: First arrow goes left from 4 to 2, second arrow goes right from 2 to 6. This starts near 3.5 (close to 4), moves left (like subtracting), then right again. 7. Since the expression is a single movement left from 3.5 to -2.5, none of the graphs perfectly match the exact movement, but Graph A shows a left movement starting near -2, which is close to the result. Graph C shows a left then right movement starting near 4, which is inconsistent with the expression. Graph B only moves right. 8. Therefore, the best representation is Graph A, which shows a left movement consistent with adding a negative number. **Final answer:** Graph A represents the expression $3 \frac{1}{2} + (-6)$ correctly.