1. **Problem Statement:** We need to sketch the graphs of the inequalities: a. $3x - 3 < y$ b. $3 > y$ c. $3x - 2y \leq 6$ d. $x^2 - y \leq 9$ 2. **Understanding each inequality:** - For (a), the inequality $3x - 3 < y$ means the region above the line $y = 3x - 3$, but not including the line itself (dashed boundary). - For (b), $3 > y$ means $y < 3$, so the region below the horizontal line $y = 3$, not including the line (dashed boundary). - For (c), $3x - 2y \leq 6$ can be rewritten to express $y$: $$3x - 2y \leq 6 \implies -2y \leq 6 - 3x \implies y \geq \frac{3x - 6}{2}$$ This means the region above or on the line $y = \frac{3x - 6}{2}$ (solid boundary). - For (d), $x^2 - y \leq 9$ can be rewritten as: $$-y \leq 9 - x^2 \implies y \geq x^2 - 9$$ This is the region above or on the parabola $y = x^2 - 9$ (solid boundary). 3. **Summary of boundaries and regions:** - (a) Line: $y = 3x - 3$, region above, dashed line. - (b) Line: $y = 3$, region below, dashed line. - (c) Line: $y = \frac{3x - 6}{2}$, region above or on, solid line. - (d) Parabola: $y = x^2 - 9$, region above or on, solid curve. 4. **Graphing notes:** - Dashed lines indicate the boundary is not included. - Solid lines indicate the boundary is included. - Regions are shaded accordingly. 5. **Final expressions for graphing:** - (a) $y > 3x - 3$ - (b) $y < 3$ - (c) $y \geq \frac{3x - 6}{2}$ - (d) $y \geq x^2 - 9$ These inequalities describe the shaded regions on their respective graphs.