Calculate the ratio in which the line joining A(6, 5) and B(4, -3) is divided by the line y = 2.

Let point of intersection be (x, 2) [∵ any point on the line y = 2 has y co-ordinate = 2]

By formula,

$y = \dfrac{m$1y2 + m2y1}{m1 + m2} \\[1em] \Rightarrow 2 = \dfrac{m1 \times -3 + m2 \times 5}{m1 + m2} \\[1em] \Rightarrow 2m1 + 2m2 = -3m1 + 5m2 \\[1em] \Rightarrow 2m1 + 3m1 = 5m2 - 2m2 \\[1em] \Rightarrow 5m1 = 3m2 \\[1em] \Rightarrow \dfrac{m1}{m2} = \dfrac{3}{5}.

m₁ : m₂ = 3 : 5.

Hence, ratio = 3 : 5.