1. **State the problem:** We need to find the gradient of the line PQ where P is at (3,16) and Q is at $(3+h, y)$ on the curve $y = x^2 + 3x - 2$. 2. **Find the coordinates of Q:** Since Q lies on the curve, substitute $x = 3 + h$ into the equation: $$y = (3+h)^2 + 3(3+h) - 2$$ 3. **Expand and simplify:** $$(3+h)^2 = 9 + 6h + h^2$$ $$3(3+h) = 9 + 3h$$ So, $$y = 9 + 6h + h^2 + 9 + 3h - 2 = (9 + 9 - 2) + (6h + 3h) + h^2 = 16 + 9h + h^2$$ 4. **Calculate the gradient of line PQ:** The gradient formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $P = (3,16)$ and $Q = (3+h, 16 + 9h + h^2)$. So, $$m = \frac{(16 + 9h + h^2) - 16}{(3 + h) - 3} = \frac{9h + h^2}{h}$$ 5. **Simplify the expression:** $$m = \frac{h(9 + h)}{h} = 9 + h$$ **Final answer:** The gradient of the line PQ in terms of $h$ is $$m = 9 + h$$