the numerator has a degree of 1, the denominator has a degree of 1 as well.
the coefficient for the leading term in the numerator is -2,
the coefficient for the leading term in the denominator is 1,
the horizontal asymptote is at y = -2/1.
in short, if the numerator and denominator are of the same degree, the horizontal asymptote is just the fraction from their leading term's coefficient.
