Proportions?

[Dillinger4]

Ive been looking at some problems dealing with proportions lately and from what i understand if an object is proportional it is said to be in direct variation or directy proportional. If the object is not proportional it is said to be in indirect variation or inversely proportional.

Indirect variation y = k / x
Direct variation y = kx

Now with the indirect variation formula i can see that when x increases y decreases. This seems natural since we are dividing the constant k by a increasing divisor.

Now for the direct variation formula it seems that in order to acheive proportion a constant of one would have to be used.

y = kx
2 = 1 * 2
3 = 1 * 3

I cant see how proportion would be acheived any other way. Any help or suggestions would be great.

[NotLKH]

Direct proportion, IE, K, signifies that for an increase in X there is an equivalant increase in Y. It doesn't have to be 1:1, but the K represents that it could be any increase, since its constant.
could be 1:2, could be 1.9),

Inversely proportional is a misnomer. It is Identical to "Directly" proportional, except k is > -1 and < 1.

Don't overthink it. Along with many other math rules.
Alot of it is really simple. Overthinking it hides the simplicity.




-Lou

[Dillinger4]

Posted by NotLKH
Direct proportion, IE, K, signifies that for an increase in X there is an equivalant increase in Y. It doesn't have to be 1:1, but the K represents that it could be any increase, since its constant.
could be 1:2, could be 1.9),

I see what you are saying about it not having
to be a 1:1 ratio. It makes sense. I guess i was
thinking that for somthing to be proportional the
ratio had to be 1:1. Like having a cube with the
same width and height.
Thanks for the help Lou.

[RAEsquivelC]

Lou, you wrote:
============================================
"Inversely proportional is a misnomer. It is Identical to "Directly" proportional, except k is > -1 and < 1."
============================================
Am I to understand that, if k = 0.5 (0.5 > -1 and < 1), then

y = 0.5 / x

is to be read, "y is directly proportional to x"??? Not in my book! You must have meant something else, but, I couldn't reach any conclusion about it. Perhaps you could clarify? Thanks.