Question

Find the equation of a line which makes an angle of tan⁻¹ (3) with the x-axis and cuts off an intercept of 4 units on negative direction of y-axis.

Answer 1

Let m be the slope of the required line.
$$\begin{gathered} \therefore m=\tan \theta =\tan \left\{{\tan }^{-1}\left(3\right)\right\}=3 \\ c=y-\mathrm{intercept}=-4 \end{gathered}$$

Substituting the values of m and c in y = mx + c, we get y = 3x $-$ 4

Hence, the equation of the required line is y = 3x $-$ 4