We have a slant asymtote because the degree of the numerator is greater than the degree of the denominator. We would find the slant asymptote by dividing the polynomial. We would apply the method of long division. the steps are shown below
The first step was to divide 3x^2 by x. We got 3x and multiplied it by x - 2. We got 3x^2 - 6x which we subtracted from 3x^2 - 8x + 1 and got - 2x + 1
the process was repeated until we got a remainder of - 3
The equation of the slant asymptote is the result of the division and the remainder is not included.
Thus, equation of slant asymptote is
y = 3x - 2