Question

What is the difference between:

- This is proportional to...

- This is directly proportional to...

^- assume I am talking about two variables
(ex. P, or T, or V etc.)

Answer 1

Well, actually there is technically a little more information in one than the other.

DIRECTLY proportional means that one variable varied 'directly proportionately to' another variable.

e.g.

a is directly proportional to b
x is directly proportional to y
d is directly proportional to t

So, for the first one....a is directly proportional to be means that if you double 'a', you also double 'b'. If you take half of 'a', you also take half of 'b'...and so on.

But you can have differing types of proportionalities.

You can have the inverse proportionality.

e.g

a is inversely proportional b...meaning a is proportional to 1/b

--or--

You can have a variable that varies as the square, or cube or logarithm of another, and so on.

e.g.

a is proportional to the natural log of b....a is proportional to Ln(b)
a is proportional to the cube of b....a is proportional to b³
a is proportional to the square root of b....a is proportional to √b

....and so on.

Do you see how saying "directly" proportional has a specific meaning, but the other can be more general?

It may be splitting hairs, but when communicating information in science, the language chosen and the communication should be kept standard so, when used, it carries the proper meaning to others.

Answer 2

i hope it will help u 2

Answer 3

There is one question I REALLY need help with. I am going to post it as a new question