Question

Two lines passing through the point (2, 3) make an angle of 45°. If the slope of one of the lines is 2, then find the slope of the other line.

Answer 1

Let m₁ and m₂ be the slopes of the two lines. 

Then, m₁ = 2, m₂ =? 

We have tan 45° = \(\frac{m_1-m_2}{1+m_1m_2}\)

⇒ 1 = \(\frac{2-m_2}{1+m_2}\)

⇒ 1 + 2m₂ = 2 – m₂

⇒ m₂ = \(\frac{1}{3}\) . 

∴ Slope of the other line = \(\frac{1}{3}\) .