Final answer:
The table showing the relationship between time and length demonstrates a proportional relationship because the ratio of length to time is constant at 1.5 for each pair of measurements.
Step-by-step explanation:
To determine if the given relationship table of time to length is proportional or nonproportional, we need to check if the ratio between them is constant. A proportional relationship would have a constant ratio, meaning that as one quantity increases, the other increases at the same rate.
Proportional relationships are characterized by a consistent ratio between two quantities. For example, if we look at the proposed times of 5, 10, 15, and 20, and their corresponding lengths of 7.5, 15, 22.5, and 30 inches, we can set up ratios to compare these values:
- Time: 5 - Length: 7.5 (ratio: 7.5/5 = 1.5)
- Time: 10 - Length: 15 (ratio: 15/10 = 1.5)
- Time: 15 - Length: 22.5 (ratio: 22.5/15 = 1.5)
- Time: 20 - Length: 30 (ratio: 30/20 = 1.5)
Since all ratios simplify to 1.5, this indicates a constant ratio, hence the relationship is proportional.