If the angle between the lines is frac{pi}{4} | vedclass

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(A) Given $	heta = \frac{\pi}{4} = 45^{\circ}$ and $m_1 = \frac{1}{2}$.Using the formula for the angle between two lines:$	an 	heta = \left| \frac{

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$3$ or $-\frac{1}{3}$

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(A) Given $	heta = \frac{\pi}{4} = 45^{\circ}$ and $m_1 = \frac{1}{2}$.Using the formula for the angle between two lines:$	an 	heta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} ight|$$	an 45^{\circ} = \left| \frac{\frac{1}{2} - m_2}{1 + \frac{1}{2} m_2} ight|$$1 = \left| \frac{1 - 2m_2}{2 + m_2} ight|$This implies $\frac{1 - 2m_2}{2 + m_2} = 1$ or $\frac{1 - 2m_2}{2 + m_2} = -1$.Case $1$: $1 - 2m_2 = 2 + m_2$ $\Rightarrow -3m_2 = 1$ $\Rightarrow m_2 = -\frac{1}{3}$.Case $2$: $1 - 2m_2 = -(2 + m_2)$ $\Rightarrow 1 - 2m_2 = -2 - m_2$ $\Rightarrow m_2 = 3$.Thus,the slope of the other line is $3$ or $-\frac{1}{3}$.

If the angle between the lines is $\frac{\pi}{4}$ and the slope of one of the lines is $\frac{1}{2}$,then the slope of the other line is

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