What is the horifzontal asymptote?

It is a horizontal line that a graph approaches but never quite reaches.

if I was on my computer I would show you with a picture. :(

This graph has a horizontal asymtote at y=-1

https://www.desmos.com/calculator/mzwrhtmryz

Let me add someting here.....it IS possible for a graph to cross its horizontal asymptote but it is NOT POSSIBLE for it to cross a vertical asymptote.

Here's the graph of y = (5x + 9) / (x^2 - 3x - 18) ........https://www.desmos.com/calculator/gfbipbzn1b

Notice that - as a consequence of a "low over high" situation - it has a horizontal asymptote at y = 0, but that it crosses this asymptote at x = -9/5......!!!!!!