Case I:
Line not passing through origin. Let the equation of the line be x/a + y/b = 1 …….(i)
This line passes through A(3, 5).
∴ 3/a + 5/b = 1 ……..(ii)
Since the required line makes equal intercepts on the co-ordinates axes,
a = b …….(iii)
Substituting the value of b in (ii), we get 3/a + 5/a = 1
∴ a = 8
∴ b = 8 …… [From (iii)]
Substituting the values of a and b in equation (i), the equation of the required line is x/8 + y/8 = 1
∴ x + y = 8
Case II:
Line passing through origin. Slope of line passing through origin and A(3, 5) is m = 5-0/ 3-0 = 5/3
∴ Equation of the line having slope m and passing through origin (0, 0) is y = mx.
∴ The equation of the required line is y = \(\frac {5}{3}\times\)
∴ 5x – 3y = 0
