Given:
a.) y = 2.5 when x = 9
Let's find the constant of variation (k).
For us to be able to determine which of the given choices is the answer, let's plugin x = 2.5 and y = 9 in each of them to see if it will make the equation correct.
CHOICE A: k = 22.5 ; y = 22.5x
2.5 = 22.5(9)
2.5 ≠ 202.5 (False)
Choice A is not the answer
CHOICE B: k = 3.6 ; xy = 3.6
(2.5)(9) = 3.6
22.5 ≠ 3.6 (False)
Choice B is not the answer
CHOICE C: k = 3.6 ; y = 3.6/x
2.5 = 3.6/9
2.5 ≠ 0.4 (False)
Choice C is not the answer
CHOICE D: k = 22.5 ; xy = 22.5
(2.5)(9) = 22.5
22.5 = 22.5 (True)
Choice D is the answer
Therefore, the answer is CHOICE D.