Directly proportional to which?

This might be a simple question, but the exact wording of this statement is important. If I know that the relationship between two variables is this:

$$\gamma \propto \frac{1}{\sqrt{k}}$$

Is the appropriate way to write that in a sentence: 'y is inversely proportional to k' or should it be 'y is inversely proportional to the square root of k'.

If somebody could explain why whichever is correct is correct, that would be great.

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1 Answer

I would take "$y$ is inversely proportional to $k$" to mean $y=c/k$ for some constant $c$, so for your situation I'd definitely say "$y$ is inversely proportional to the square root of $k$."

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Okay, but you would still say that 'the relationship between y and k is inversely proportional'? (slightly different wording) – user10265 May 21 '11 at 11:48
@user10265: I wouln't, and I hope no careful person would. One might say "there is an inverse relationship" to mean that as one increases, the other decreases. – André Nicolas May 21 '11 at 13:45