Final answer:
Upon analyzing the given data pairs for constant ratios, it's clear that the ratios are not consistent, thus this is not an example of direct variation.
Step-by-step explanation:
To determine if the given relationship represents direct variation, we should check whether the ratio of the dependent variable to the independent variable is consistent across all pairs of data. Direct variation implies that as the independent variable increases, the dependent variable increases at a constant rate, represented mathematically by the equation y = kx, where k is the constant of variation.
Let's examine the given data pairs: (1, 10), (2, 12), (3, 16), (4, 22), (5, 30). To see if these are examples of direct variation, we will calculate the ratio of y to x for each pair:
- For (1, 10), the ratio is 10/1 = 10.
- For (2, 12), the ratio is 12/2 = 6.
- For (3, 16), the ratio is 16/3 ≈ 5.33.
- For (4, 22), the ratio is 22/4 = 5.5.
- For (5, 30), the ratio is 30/5 = 6.
Since the ratios are not consistent, we can conclude that this is not an example of direct variation.