1. **Problem Statement:** Find the slope of the secant line to the curve $n(x) = 3x^2 - 2$ passing through the points $(1, n(1))$ and $(2, n(2))$. 2. **Formula:** The slope $m$ of the secant line between points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate $n(1)$ and $n(2)$:** $$n(1) = 3(1)^2 - 2 = 3 - 2 = 1$$ $$n(2) = 3(2)^2 - 2 = 3 \times 4 - 2 = 12 - 2 = 10$$ 4. **Substitute values into the slope formula:** $$m = \frac{10 - 1}{2 - 1} = \frac{9}{1}$$ 5. **Simplify:** $$m = 9$$ **Final answer:** The slope of the secant line is $9$.