Question

find the equation of the line which is inclined at 30 degree with the negative direction of the y-axis and cuts off an intercept 2 on the x-axis in the negative direction of the x-axis.

Answer 1

$$\begin{gathered} \mathrm{As}\mathrm{line}\mathrm{making}\mathrm{angle}\mathrm{of}30°\mathrm{with}\mathrm{negative}\mathrm{y}-\mathrm{axis}\mathrm{in}\mathrm{the}\mathrm{direction}\mathrm{of}\mathrm{negative}\mathrm{x}-\mathrm{axis}. \\ \mathrm{Then}\mathrm{it}\mathrm{will}\mathrm{make}120°\mathrm{with}\mathrm{positive}\mathrm{x}-\mathrm{axis}. \\ \mathrm{m}=\tan 120°=\tan \left(90+30\right)° \\ =-\cot 30°=-\sqrt{3}. \\ \mathrm{As}\mathrm{line}\mathrm{cuts}\mathrm{off}\mathrm{an}\mathrm{intercept}2\mathrm{on}\mathrm{the}\mathrm{x}-\mathrm{axis},\mathrm{So}\mathrm{it}\mathrm{will}\mathrm{pass}\mathrm{through}\left(2,0\right). \\ \frac{\mathrm{y}-0}{\mathrm{x}-2}=-\sqrt{3} \\ \mathrm{y}=-\sqrt{3}\mathrm{x}+2\sqrt{3} \\ \mathrm{y}+\sqrt{3}\mathrm{x}=2\sqrt{3}\mathrm{ANS}... \end{gathered}$$