Find the equation of a straight line which passes through the point $\left(-1, 2\right)$ and is inclined at $60^\circ$ to the $X$ axis.
Inclination of the required line to the $X$ axis $= \theta = 60^\circ$
$\therefore \;$ Slope of the required line $= m = \tan \theta = \tan 60^\circ = \sqrt{3}$
The required line passes through the point $\left(x_1, y_1\right) = \left(-1, 2\right)$
Equation of the required line is of the form: $\;$ $y - y_1 = m \left(x - x_1\right)$
$\therefore \;$ The equation of the required line is
$y - 2 = \sqrt{3} \left(x + 1\right)$
i.e. $\;$ $\sqrt{3} x - y + \sqrt{3} + 2 = 0$