Inclined asymptote can be found by calculating the limit of log(1/3)*(x + 1), divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\left(x + 1\right) \log{\left(\frac{1}{3} \right)}}{x}\right) = - \log{\left(3 \right)}$$
Let's take the limitso,
inclined asymptote equation on the left:
$$y = - x \log{\left(3 \right)}$$
$$\lim_{x \to \infty}\left(\frac{\left(x + 1\right) \log{\left(\frac{1}{3} \right)}}{x}\right) = - \log{\left(3 \right)}$$
Let's take the limitso,
inclined asymptote equation on the right:
$$y = - x \log{\left(3 \right)}$$