Final answer:
The constant of proportionality (K) for the given set of values is 0.6, as the ratio of Y to X is the same for all given pairs of values.
Step-by-step explanation:
To find the constant of proportionality (K) for the given sets of values, we need to verify that the ratio Y/X is constant for all the given pairs of X and Y. If a constant of proportionality exists, it implies that Y is directly proportional to X. The concept of proportionality is a fundamental aspect of ratios and linear functions in mathematics.
The given pairs of values are (X:7.5, Y:4.5), (X:10, Y:6), (X:17.5, Y:10.5), and (X:20, Y:12).
- For the first pair, K = Y/X = 4.5/7.5 = 0.6
- For the second pair, K = Y/X = 6/10 = 0.6
- For the third pair, K = Y/X = 10.5/17.5 = 0.6
- For the fourth pair, K = Y/X = 12/20 = 0.6
Since the ratio Y/X is the same for all pairs, the constant of proportionality K is 0.6.