Why Do We Introduce Constants in Proportional Relationships?

[StupidGenius]

My proff mentioned something about proportionality:
"To make an a proportionality into an equality, we must introduce a constant"
Something along those words: my question is why? Can show prove this to me??

 

[Hootenanny]

My proff mentioned something about proportionality:
"To make an a proportionality into an equality, we must introduce a constant"
Something along those words: my question is why? Can show prove this to me??

I am not aware of any proof of the concept, but I can offer a reason. Consider the statement "y is proportional to x". This means that a finite change in x induces a finite change in y. The size of the change in y depends on the size of the change in x. Now to quantify it, we need to introduce the so-called constant of proportionality. It is this constant that determines how big the change in y is for a given change in x.

For example, take the equation y = 3x. Clearly y is proportional to x and if x changes by +1, then y changes by +3. Equally, consider the equation y = 2x. Once again, y is clearly proportional to x, but this time for each integer step of x, y changes by 2.

This is why we need to introduce such constants. More technically, a proportionality defines a family of curves, by fixing the constant of proportionality (as well as the additive constant) you are effectively choosing a single curve from the family.