If x ix directly proportional to y then ...

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Question from Crystal, a student:

I understand that we say x and y are proportional, then y = kx.
Generally when we say x is proportional to y, we think that when x increases y increases.
Now I am questioning whether that is actually true.
If k is negative, then when x increases, y DECREASES.
My question is does this mean this statement is incorrect:
If x is proportional to y, when x increases, y increases proportionally.
Is it more correct to say:
If x is proportional to y, when x increases, y either increases proportionally or decreases proportionally.
Along the same line of reasoning, when x is inversely proportional to y,
we think that when x increases y decreases, but that is true only if k is positive.
Is that correct?

Hi Crystal,

You are correct Crystal. I have been guilty of that myself, saying that if x is directly proportional to y then if x increases so does y. I think what I should be saying is that if the magnitude of x increases then the magnitude of y increases. By the magnitude I mean the absolute value. Similarly if x is inversely proportional to y then as the magnitude of x increases the magnitude of y decreases.

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.