Final answer:
By dividing each y value by its corresponding x value and finding the same ratio of 3.5, we identify the constant of proportionality relating x and y as 3.5, meaning y is directly proportional to x.
Step-by-step explanation:
To find the constant of proportionality that relates x and y based on the provided values, we can divide the y value by the corresponding x value for each pair of numbers in the table. If this ratio is consistent across all pairs, that ratio is the constant of proportionality.
- Divide 21 by 6: 21 ÷ 6 = 3.5.
- Divide 24.5 by 7: 24.5 ÷ 7 = 3.5.
- Divide 28 by 8: 28 ÷ 8 = 3.5.
- Divide 31.5 by 9: 31.5 ÷ 9 = 3.5.
Since the result is the same for each pair of values, the constant of proportionality for the table of values is 3.5. This indicates that y is directly proportional to x, and the equation relating x and y would be y = 3.5x.