1. **Stating the problem:** We are given two points on a line representing the investment amount $A$ over time $t$: $(3, 16500)$ and $(6, 18000)$. We want to find the linear equation $A = mt + b$ that models this relationship. 2. **Formula used:** The equation of a line is $A = mt + b$, where $m$ is the slope and $b$ is the intercept (value of $A$ when $t=0$). 3. **Calculate the slope $m$:** $$m = \frac{A_2 - A_1}{t_2 - t_1} = \frac{18000 - 16500}{6 - 3} = \frac{1500}{3} = 500$$ 4. **Find the intercept $b$:** Use one point, for example $(3, 16500)$: $$16500 = 500 \times 3 + b$$ $$16500 = 1500 + b$$ $$b = 16500 - 1500 = 15000$$ 5. **Write the equation:** $$A = 500t + 15000$$ 6. **Interpretation:** The investment starts at 15000 when $t=0$ and increases by 500 each year. **Final answer:** $$\boxed{A = 500t + 15000}$$