Question

If the angle between two lines is $\pi /4$ and slope of one of the line is $1/2$, find the slope of the other line.

Answer 1

Let the slope be $m_1$ and $m_2$

and $\theta =\frac{\pi }{4}$

$tan\theta =|\frac{m_1-m_2}{1-m_1{m}_2}|$

$tan\frac{\pi }{4}=1=|\frac{\frac{1}{2}-m_2}{1+\frac{1}{2}{m}_2}|$

$\frac{\frac{1}{2}-m_2}{1+\frac{1}{2}{m}_2}=\pm 1$

$\frac{\frac{1}{2}-m_2}{1+\frac{1}{2}{m}_2}=1$ or $\frac{\frac{1}{2}-m_2}{1+\frac{1}{2}{m}_2}=-1$

$m_2+\frac{m_2}{2}=-\frac{1}{2}$ or $\frac{1}{2}-m_2=-1-\frac{m_2}{2}$

$m_2=-\frac{1}{3},3$