1. The problem is to determine if given ordered pairs are solutions to the inequality derived from the line equation $y = 2 - \frac{3x}{2}$ and to prove algebraically that $(2,1)$ is not a solution. 2. The inequality is not explicitly given, but the shaded region is mostly in the lower-right side, suggesting the inequality is $y \leq 2 - \frac{3x}{2}$ (below or on the line). 3. To check if an ordered pair $(x,y)$ is a solution, substitute $x$ and $y$ into the inequality and verify if it holds true. 4. Check $(4,0)$: $$0 \leq 2 - \frac{3(4)}{2} = 2 - 6 = -4$$ Since $0 \leq -4$ is false, $(4,0)$ is NOT a solution. 5. Check $(0,0)$: $$0 \leq 2 - \frac{3(0)}{2} = 2 - 0 = 2$$ Since $0 \leq 2$ is true, $(0,0)$ is a solution. 6. Prove algebraically that $(2,1)$ is NOT a solution: Substitute $x=2$, $y=1$ into the inequality: $$1 \leq 2 - \frac{3(2)}{2} = 2 - 3 = -1$$ Since $1 \leq -1$ is false, $(2,1)$ is NOT a solution. 7. Summary: - $(4,0)$ is NOT a solution. - $(0,0)$ is a solution. - $(2,1)$ is NOT a solution. This matches the shaded region being below or on the line $y = 2 - \frac{3x}{2}$.