# Negative Direct Variation

## Homework Statement

Alright, so I just want some clarification on direct variation, since it seems that every internet source I can find is (seemingly to me) wrong.

To me, direct variation means that the ratio of y to x is fixed with y=kx where k is the constant of proportionality.

Various sources online say that this means as y increases so does x or as y decreases so does x. BUT, I think this is wrong for the following reason.

If k is negative such that y=-kx, then as x increases y will DECREASE. However, if you take a bunch of co-ordinates and find the proportion of y to x, you get a negative constant (-k). Therefore they must be directly proportional. I think of this as a negative slope to a line, the line shows that the co-ordinates are proportional, but as x increases, y decreases.

So am I correct? Can the constant of proportionality k be negative and show direct variation? If not why not?

y=kx, y=-kx

(see above)

## Answers and Replies

statdad
Homework Helper
"Can the constant of proportionality k be negative and show direct variation?"

Yes. Y is directly proportional to x if there is a constant k such that Y = kX. NO mention need be made of whether k is positive or negative.

Alright, thanks for the help! There seems to be an awful lot of technically incorrect online resources on this. :P