The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find :

(i) the equation of AB;

(ii) the co-ordinates of the point where the line AB intersects the y-axis.

(i) $\text{Slope of AB } = \dfrac{y$2 - y1}{x2 - x1} \\[1em] = \dfrac{-1 - 4}{2 - (-3)} \\[1em] = \dfrac{-5}{5} \\[1em] = -1.

Equation : y - y₁ = m(x - x₁)

⇒ y - 4 = (-1)[x - (-3)]

⇒ y - 4 = -1(x + 3)

⇒ y - 4 = -x - 3

⇒ y + x = -3 + 4

⇒ x + y = 1.

Hence, equation of AB is x + y = 1.

(ii) The point where AB intersects y-axis, there x co-ordinate = 0.

Substituting x = 0 in equation of AB we get,

⇒ 0 + y = 1

⇒ y = 1.

Point = (x, y) = (0, 1).

Hence, co-ordinates of the point where AB intersects the y-axis = (0, 1).