To analyze the provided data for \(x\) and \(y\) and determine the type of association, let's first summarize the values:
Values of \(x\):
- 25, 30, 80, 150, 250, 350, 425, 450, 500
Values of \(y\):
- 375, 225, 120, 75, 50, 100, 175, 275, 400
Next, we can examine the relationship between the pairs of values:
- For smaller values of \(x\) (25 and 30), \(y\) starts high (375, 225).
- As \(x\) increases, \(y\) initially decreases, reaching its minimum at \(x = 250\) (when \(y = 50\)).
- Then, for larger \(x\) values, \(y\) starts increasing again from \(y = 50\) at \(x = 250\) to \(y = 400\) at \(x = 500\).
From this observation, we see that \(y\) does not change in a linear manner with \(x\); rather, it decreases initially and then increases. This suggests a non-linear relationship.
Thus, the association can be determined as non-linear association.
The correct response from the options given would be: non-linear association.