Question

Find the angle between the following straight lines.
y = 4 – 2x, y = 3x + 7​

Answer 1

$\textbf{Given:}$

$\textsf{Lines are}$

$\mathsf{2x+y-4=0\;and\;3x-y+7=0}$

$\textbf{To find:}$

$\textsf{Angle between the given lines}$

$\textbf{Solution:}$

$\mathsf{Slope\;of\;2x+y-4=0\;is\;m_1=\dfrac{-2}{1}=-2}$

$\mathsf{Slope\;of\;3x-y+7=0\;is\;m_2=\dfrac{-3}{-1}=3}$

$\textsf{The angle between the given lines is}$

$\mathsf{tan\theta=\left|\dfrac{m_1-m_2}{1+m_1m_2}\right|}$

$\mathsf{tan\theta=\left|\dfrac{-2-3}{1+(-2)(3)}\right|}$

$\mathsf{tan\theta=\left|\dfrac{-5}{1-6}\right|}$

$\mathsf{tan\theta=\left|\dfrac{-5}{-5}\right|}$

$\mathsf{tan\theta=\left|1\right|}$

$\mathsf{tan\theta=1}$

$\implies\boxed{\mathsf{\theta=\dfrac{\pi}{4}\;(or)\;45^\circ}}$

$\textbf{Find more:}$

Find the acute angle between the lines 12x-4y=5 and 4x+2y=7​

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