why do we take proportionality constants?

Becuase we are talking of ratios basically.

When we say the ratio of two quantities is same, we take an instance of two quantities take the ratio and equate it to another instance, say 4/8 = 6/12,

But instead, if we choose to keep another instance of the quantities as variables, we get,

4/8 = x/y

and we can write,

y = 2x,

Now we just establish a relation between the two quantities,

and paraphrase it as, y is propotional to x, and immediately we recognize 2 as the propotionality constant.

Regards,

Team,

TopperLearning.