Question

Find the equation of the line that passes though $(2, 2\sqrt 3)$ and is inclined with the x-axis at an angle of 75°.

Answer 1

The slope of the line that inclines with the x-axis at an angle of 75° is
$m = tan \ 75°$
⇒ $m=tan(45°+30°)$ = $\frac {tan\ 45°+tan\ 30°}{1-tan\ 45°tan\ 30°}$ = $\frac {1+\frac {1}{\sqrt 3}}{1-1.\frac {1}{\sqrt 3}}$= $\frac {\sqrt 3+1}{\sqrt 3-1}$
We know that the equation of the line passing through point $(x_0, y_0)$, whose slope is m, is $(y-y_0)=m(x-x_0)$
Thus, if a line passes though $(2,2\sqrt 3)$ and inclines with the x-axis at an angle of 75°, then the equation of the line
is given as