# Equations of Algebraic Curves
Please do not write as y=mx+n if you want to do geometry, not
analysis. I know you can easily draw the graphs with that form,
because y is a function of x. But please don't do aside from that.
It feels really weird. Write it as y-mx-n=0, or p(x,y)=0, even
better.
The main point is that a prime ideal corresponds to an affine
variety. The prime ideal (y-mx-n) corresponds to the line. It's
all about algebra corresponding to geometry. That is the central
theme of algebraic geometry.