How many different ways can a line be named?

Answer 1

There are very many ways which depend on the level of your mathematical sophistication.

1. slope intercept form: y = mx + c
2. two point form: (y2 - y1)/(x2 - x1) = (y - y1)/(x - x1) where x2 is not equal to x1
3. standard form: ax + by + c = 0 [this form can be extended to lines in spaces with 3 or more dimensions]
4. r*sin(theta) = r*m*cos(theta) + c

There are also several vector forms, but I expect that those are too advanced.