Final answer:
After calculating the ratios of y to x for each pair in the table and finding that they are not consistent, it has been determined that the relationship between x and y is not proportional.
Step-by-step explanation:
To determine if the table shows a proportional relationship, we need to check if the ratio of y to x is constant across the pairs of numbers given. Proportional relationships can also be represented by a straight line through the origin on a graph.
Given the table:
- x = 36.5, y = 18.25
- x = 23.2, y = 11.6
- x = 63.3, y = 21.1
To test for proportionality, we calculate the ratio of y/x for each pair:
- For the first pair: 18.25 / 36.5 = 0.5
- For the second pair: 11.6 / 23.2 = 0.5
- For the third pair: 21.1 / 63.3 ≈ 0.333
The ratios of the first two pairs are equal, but the third pair has a different ratio, indicating that the relationship between x and y in the table is not proportional.