Find the equation of the vertical asymptote and the equation of the slant asymptote of the rational function. \[ f(x)=\frac{-24 x^{2}-7 x+2}{3 x-1} \] The equation of the vertical asymptote is $x=$ The equation of the slant asymptote is $y=$

Step 1 ：The vertical asymptote of a rational function is found by setting the denominator equal to zero and solving for x.

Step 2 ：So, we set the denominator 3x - 1 equal to zero and solve for x, which gives us x = 1/3.

Step 3 ：The slant asymptote is found by performing long division of the numerator by the denominator.

Step 4 ：If the degree of the numerator is exactly one more than the degree of the denominator, the quotient is the equation of the slant asymptote.

Step 5 ：Performing the long division, we get the equation of the slant asymptote as y = -8x - 5.

Step 6 ：So, the equation of the vertical asymptote is \(x=\boxed{\frac{1}{3}}\) and the equation of the slant asymptote is \(y=\boxed{-8x - 5}\).