Question

Find the equation of the line through $(2,3)$ and making an angle ${30}^{\circ }$ with the y-axis

Answer 1

The point is $(2,3)$

The angle made with $x$ axis is ${90}^0-{30}^0={60}^{\circ }$

The slope of the line is $\tan {60}^0=\sqrt{3}$

General equation of line is given as,

$y-y_1=m(x-x_1)$

$\Rightarrow y-3=\sqrt{3}(x-2)$

$\Rightarrow \sqrt{3}x-y+3-2\sqrt{3}=0$