How would you mathematically describe a line infinitely close to being horizontal?

Let's say it goes through [0, 0]. Would it at the "ends" still be infinitely close to 0 as [inf, 0+] or [inf, inf]?

I mean it's not like your regular lim of a curve. It's ever so slightly tilted line and should eventually get away from 0.

But even very little tilted line going through [0, 0] and e.g. [g64, 1/g64] could be even less tilted: [g64, 1/(g64*2)].