Let $P=(-1,0)$, $Q=(0,0)$ and $R=(3,3\sqrt{3})$ be three points. The equation of the bisector of the angle $PQR$ is:

The vertex of the angle is $Q(0,0)$.$QP$ is along the negative $x$ -axis. Its inclination is $180^{\circ }$ or $\pi$.The slope of $QR$ is $m=\frac{3\sqrt{3}-0}{3-0}=\sqrt{3}$.The inclination of $QR$ is ${\tan }^{-1}(\sqrt{3})=60^{\circ }$ or $\pi /3$.The angle $PQR$ is the angle between the lines $QP$ and $QR$.The angle of the bisector is the average of the inclinations:
$$\text{Inclination}=\frac{180^{\circ }+60^{\circ }}{2}=120^{\circ }$$
The slope of the bisector is $\tan (120^{\circ })=-\sqrt{3}$.Since the bisector passes through $Q(0,0)$, its equation is:
$$y=-\sqrt{3}x⟹\sqrt{3}x+y=0$$