Question

Find the slope of the line, which makes an angle of ${30}^{\circ }$ with the positive direction of $y-axis$ measured anticlockwise.

Answer 1

$\Rightarrow$ The line makes angle of ${30}^o$ from positive $y-axis$

$\Rightarrow$ Hence, it makes angles of $({90}^o+{30}^o)$ from positive x axis $i.e.$ ${120}^o$ from positive $x-axis$

$\therefore$ $\theta ={120}^o$

$\Rightarrow$$Slope=m=\tan \theta$

$=\tan {120}^o$

$=\tan ({180}^o-{60}^o)$

$=-\tan {60}^o$

$=-\sqrt{3}$

$\therefore$ Slope of the line is $-\sqrt{3}$.