1. **State the problem:** We are given three points $(1,4)$, $(2,7)$, and $(4,13)$ representing gallons $g$ of water at time $t$ minutes. We need to determine if these points lie on the same straight line. 2. **Recall the formula for slope:** The slope $m$ between two points $(t_1,g_1)$ and $(t_2,g_2)$ is given by $$m = \frac{g_2 - g_1}{t_2 - t_1}$$ 3. **Calculate the slope between the first two points:** $$m_{12} = \frac{7 - 4}{2 - 1} = \frac{3}{1} = 3$$ 4. **Calculate the slope between the last two points:** $$m_{24} = \frac{13 - 7}{4 - 2} = \frac{6}{2} = 3$$ 5. **Calculate the slope between the first and last points:** $$m_{14} = \frac{13 - 4}{4 - 1} = \frac{9}{3} = 3$$ 6. **Interpretation:** Since $m_{12} = m_{24} = m_{14} = 3$, the slope between every pair of points is the same. 7. **Conclusion:** Because the slope is consistent between all pairs, the three points lie on the same straight line. **Final answer:** Yes, these three points lie on the same line because the slope between any two points is the same.