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Take two cases-

  • y = -x
  • y = 1/x

in both these cases as 'x' increases 'y' decreases, so according to me 'y' should be inversely proportional to 'x' in both. Please correct me if I am wrong but I also think that in first it should be 'y' is directly proportional to 'x' (from what I have read).

Kaustubh
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    "$x$ is proportional to $y$" actually means "$x/y$ is constant", not "as one increases, so does the other". – Arthur May 19 '14 at 15:42
  • @Arthur okay thanks a lot.. perhaps adding your comment as an answer would be good so I can close this question.. thnx – Kaustubh May 19 '14 at 15:44

1 Answers1

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Direct\Proportional means $y = kx$ for some constant k. Inverse means $y={k\over x}$ or $yx=k$ for some constant k (using algerbra you can see the two inverse equations are the same).

So #1 is proportional\direct because $k$ is $-1$, and #2 is inversely related because $k$ is $1$.

And yes its true that in both cases as $x$ increases $y$ decreases, but the difference actually comes from the slope type. If you notice, the proportional\direct equation $y=kx$ is always a straight line. However, the inverse relation $y={k\over x}$ is a curve of some type.

So the main difference is in the slope. One always stays the same (a line), and one changes (a curve of some type).

To tell, you just see which one the equation fits, like if $x$ is on the side opposite to $y$, and on the top, its direct ($y=kx$), if $x$ is on the bottom its inverse ($y={k\over x}$), and if $x$ and $y$ are next to each other they are inverse as well ($xy=k$).

Dane Bouchie
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