Oblique (Slant) Asymptote
Let R denote a function. If, as x approaches infinity or as x approaches negative infinity, the graph of R approaches the graph of the non-horizontal and non-vertical line y = mx + b, then y = mx + b is an oblique or slant asymptote of the graph of R.
The graph of y = (x2 + 1) / x is shown below. Notice that y = x is an oblique asymptote.