I am studying (self learner) linear equations/equation of line and my idea is to discover the equations myself rather than try and understand ready-made equations available in text books. I am using X-Y Cartesian plane, with 2 points A(x1,y1) and B(x2,y2). I know linear equations describe the relation between two points in my case Point A and Point B. So I was wondering if I come up with a definition in words and more Importantly as an Algebraic Equation; How can I make sure that my equation describes the relation Fully/Completely?! Is there a method/procedure to do this?! Also other than "completeness", are there other things/parameters a definition/description/equation is supposed to fulfill?
In addition to explaining it, any pointers, or links to relevant content are also hugely welcome.
Thanks much in Advance...