1. **Problem statement:** We want to find the correct equation for the rocket's weight $W$ at time $t$ where $0 \leq t \leq T$, given initial weight $W_1$ and final weight $W_T$ at time $T$. 2. **Understanding the problem:** The weight decreases linearly as fuel is burnt, so $W$ changes from $W_1$ at $t=0$ to $W_T$ at $t=T$. 3. **General linear equation:** A linear function from $(0, W_1)$ to $(T, W_T)$ can be written as: $$W = W_1 + m t$$ where $m$ is the slope. 4. **Calculate slope $m$:** $$m = \frac{W_T - W_1}{T - 0} = \frac{W_T - W_1}{T}$$ 5. **Substitute slope into equation:** $$W = W_1 + \frac{W_T - W_1}{T} t$$ 6. **Rewrite to show weight decrease:** Since $W_T < W_1$, rewrite as: $$W = W_1 - \frac{W_1 - W_T}{T} t$$ 7. **Check given options:** The correct formula matches: $$W = W_1 - \left(\frac{W_1 - W_T}{T}\right) t$$ **Final answer:** $$W = W_1 - \left(\frac{W_1 - W_T}{T}\right) t$$