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, 4).
∴ 3/a + 4/b = 1……………..(ii)
Since, the required line make equal intercepts on the co-ordinate axes.
∴ a = b …(iii)
Substituting the value of b in (ii), we get 3/a + 4/a = 1
∴ 7/a = 1
∴ a = 7
∴ b = 7 …[From (iii)]
Substituting the values of a and b in (i), equation of the required line is x/7 + y/7 = 1 = 1
∴ x + y = 7
Case II: Line passing through origin.
Slope of line passing through origin and A(3,4) is m = 4-0/ 3-0 = 4/3
∴ Equation of the line having slope m and passing through origin (0, 0) is y = mx.
∴ The equation of the required line is 4
y = \(\frac{4}{3}\times\)
∴ 4x – 3y = 0
