Sorry for posting this, but I really need help to understand how things are going behind.

lets assume I was solving a problem in math, I arrived to equation X^2+y^2=M^2 which the logic of that problem tells me that I could use that equation Y=aX+b which a=2, b=5 !

my case is that .. can I assign in my equation X^2+y^2=M^2 , y=2X+5 ? if yes, then why?! why I'm not for example assigning the general equation Y=aX+b with any parameters (a,b) to my equation .. why exactly it's not allowed?

once again I'm not claiming that's wrong ! but I'm not convinced how from general equation Y=aX+b over specific parameters I can assign to my problem .. ! how is that logically correct?!

thanks alot