1. **State the problem:** We need to complete the table showing the pieces of bamboo Ling Ling eats over time, where the pieces eaten each minute are represented as a multiplication by $\frac{3}{2}$, except at minute 4 where the total is 6. 2. **Understand the relationship:** The table suggests a constant rate of bamboo eaten per minute, $\frac{3}{2}$ pieces, except at minute 4 where the total pieces eaten is 6. 3. **Check the value at minute 4:** Given $y = \frac{3}{2} \times x$, at $x=4$ we calculate: $$y = \frac{3}{2} \times 4 = \frac{3}{2} \times 4 = \frac{3 \times 4}{2} = \frac{12}{2} = 6$$ This matches the given value, confirming the formula. 4. **Complete the table:** Using $y = \frac{3}{2} x$, calculate for each $x$: - $x=0$: $y = \frac{3}{2} \times 0 = 0$ - $x=1$: $y = \frac{3}{2} \times 1 = \frac{3}{2} = 1.5$ - $x=2$: $y = \frac{3}{2} \times 2 = 3$ - $x=3$: $y = \frac{3}{2} \times 3 = \frac{9}{2} = 4.5$ - $x=4$: $y = 6$ (given) - $x=5$: $y = \frac{3}{2} \times 5 = \frac{15}{2} = 7.5$ 5. **Summary:** The pieces of bamboo eaten increase linearly by $\frac{3}{2}$ pieces per minute. Final completed table: | Time (minutes) | Pieces of Bamboo | |----------------|------------------| | 0 | 0 | | 1 | $\frac{3}{2}$ | | 2 | 3 | | 3 | $\frac{9}{2}$ | | 4 | 6 | | 5 | $\frac{15}{2}$ |