Question

what is the real characteristic of slanted asymptote ?...

Answer 1

Slanted, or oblique, asymptotes are very much the same as usual horizontal asymptotes. It is a line that the graph will continously approach as x moves to infinity, the only difference is that these slanted asymptotes are, well, slanted (not horizontal). It usually happens when the degree of the numerator is bigger than the degree of the denominator.