1. **State the problem:** Determine if the point $(1,-2)$ satisfies the inequality $y \geq -6x - 3$. 2. **Substitute the point into the inequality:** Replace $x$ with $1$ and $y$ with $-2$ in the inequality. $$-2 \geq -6(1) - 3$$ 3. **Simplify the right side:** $$-2 \geq -6 - 3$$ $$-2 \geq -9$$ 4. **Check the inequality:** Since $-2$ is greater than $-9$, the inequality holds true. 5. **Conclusion:** The point $(1,-2)$ is a solution to the inequality $y \geq -6x - 3$.