Find the slope of the line making an inclination of $60^{\circ}$ with the positive direction of the $x$-axis.

Find the equation of a line that makes an angle of $60^{\circ}$ with the $x$-axis and makes an intercept of $5$ units on the negative direction of the $y$-axis.

If a straight line passing through the point $P(-3, 4)$ is such that its intercepted portion between the coordinate axes is bisected at $P,$ then its equation is

If $(0, 0)$,$(-2, 1)$,and $(5, 2)$ are the vertices of a triangle,then the equation of the line passing through the centroid and parallel to the line $x - 2y = 6$ is:

Find the equations of the sides $QR$ and $RP$ of a triangle $PQR$ where $P = (2, 1)$,and the sides $QR$ and $RP$ have slopes $m_1 = \frac{2}{\sqrt{3}}$ and $m_2 = -\frac{2}{\sqrt{3}}$ respectively,passing through the origin $(0, 0)$ for $QR$ and intersecting at $P(2, 1)$ for $RP$.

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point $(2,3)$.