Solution:

Given, co-ordinates of points E and F are (0, 4) and (3, 7) respectively

(i) The gradient of EF

m = y₂ – y₁ / x₂ – x₁ = (7 – 4)/(3 – 0) = 3/3

⇒ m = 1

(ii) Equation of line EF is given by,

y – y₁ = m (x – x₁)

y – 7 = 1 (x – 3)

y – 7 = x – 3

x – y + 7 – 3 = 0

Hence, the equation of line EF is x – y + 4 = 0