A slant asymptote, also known as an oblique asymptote, is an asymptote that's a straight (but not horizontal or vertical) line of the usual form y = mx + b (in other words, a degree-1 polynomial). A function with a slant asymptote might look something like this:
If a function f(x) has a slant asymptote as x approaches ∞, then the limit 
does not exist, because the function must grow without bound to stay close to the slant asymptote.