# Equations of Algebraic Curves
Please do not write as y=mx+n if you want to do geometry, not anal
ysis. I know you can easily draw the graphs with that form, becaus
e y is a function of x. But please don't do aside from that. It fe
els 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 vari
ety. The prime ideal (y-mx-n) corresponds to the line. It's all ab
out algebra corresponding to geometry. That is the central theme o
f algebraic geometry.