Direct Variation: If I am given the problem 3y = 4x and am

[Clapper203]

If I am given the problem 3y = 4x and I asked to find the direct variation, I know that I am supposed to divide by 3 go get it in the form of y=kx, where k is the constant of variation. Thus, the constant of variation in my example is 4/3.

But if take y=kx and you solve for k, the ratio for direct variation is y/x. So why doesn't it work to divide each side by 4x, so then you have 3y/4x to get a ratio of 3/4? The y term is being divided by the x term. I know you can't do this, but could someone explain the algebraic reasoning behind why I can't do that?

 

[tkhunny]

Reason #1 - It doesn't make any sense. Look at the definition. Direct Variation: y = kx, where k is the constant of variation. If you have (ay)/(bx) = 1, you do NOT have the definition of Direct Variation.

If you wish to define some other kind of thing, maybe "Grizwark Variation" as (ay)/(bx) = 1, feel free to do so.

Given (ay)/(bx) = 1, the Grizwark Constant is a/b.

Be prepared to explain why your definition is useful. You will have to introduce your Grizwarks to the whole Earth. It's a big job.

It's a lot simpler to go with the already-accepted definitions.