Directly Proportional vs. Inversely Proportional

ajwchin
Mon, 29 Dec 2008 17:29:58 +0000

Direct variation comes in the form of y=kx. This is where the notion of associating multiplying with direction variation comes from. However, k is the constant, so if we want to relate the variables, we have k=y/x.

Same with indirect variation; it comes in the form of y=k/x, so naturally one would associate dividing with indirect variation. But again, to directly compare the variables we need it in this form: k=yx.

That is where the confusion comes in.

So, in your problem, since we’re doing direct variation, we want k=y/x. In this case, y1=w, x1=x, y2=y, and x2=z. Since the k is the same, we can set them equal to each other:

y1/x1=y2/x2, or w/x=y/z.

Here’s another way to think about it; you said you originally thought of multiplying w and x: k=wx. Well is this direct variation? No because if we increase w (keeping k constant), x decreases, which is the definition of inverse variation.

Hope this helps :)