Write down the equation of the line whose gradient is $-\dfrac{2}{5}$ and which passes through point P, where P divides the line segment joining A(4, -8) and B(12, 0) in the ratio 3 : 1.

By section formula,

Co-ordinates of P = $\Big(\dfrac{m$1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big)

Substituting values we get,

$P = \Big(\dfrac{3 \times 12 + 1 \times 4}{3 + 1}, \dfrac{3 \times 0 + 1 \times -8}{3 + 1}\Big) \\[1em] = \Big(\dfrac{36 + 4}{4}, \dfrac{0 - 8}{4}\Big) \\[1em] = \Big(\dfrac{40}{4}, \dfrac{-8}{4}\Big) \\[1em] = (10, -2).$

By point-slope form,

Equation of line having slope = $-\dfrac{2}{5}$ and passing through P,

⇒ y - y₁ = m(x - x₁)

⇒ y - (-2) = $-\dfrac{2}{5}$[x - 10]

⇒ 5(y + 2) = -2(x - 10)

⇒ 5y + 10 = -2x + 20

⇒ 5y + 2x = 20 - 10

⇒ 2x + 5y = 10.

Hence, 2x + 5y = 10.