Solution:

Given, P divides the line segment joining the points A (-2, 6) and B (3, -4) in the ratio 2: 3

So, the co-ordinates of P will be

x = (m₁x₂ + m₂x₁)/(m₁ + m₂)

= (2×3 + 3×(-2))/ (2 + 3)

= (6 – 6)/5

= 0/5 = 0

y = (m₁y₂ + m₂y₁)/(m₁ + m₂)

= (2×(-4) + 3×(6))/ (2 + 3)

= (-8 + 18)/5 = 10/5

= 2

Hence, the co-ordinates of P are (0, 2)

Now, the slope (m) of the line passing through (0, 2) is 3/2

Thus, the equation will be

y – y₁ = m (x – x₁)

y – 2 = 3/2 (x – 0)

2y – 4 = 3x

⇒ 3x – 2y + 4 = 0