Find the equations of the lines passing through point (-2, 0) and equally inclined to the co-ordinate axes.

Let there be two lines AB and CD equally inclined to co-ordinate axes and passing through E(-2, 0).

From figure,

AB is inclined at an angle of 45°.

Slope = tan 45° = 1.

By point-slope form,

⇒ y - y₁ = m(x - x₁)

⇒ y - 0 = 1[x - (-2)]

⇒ y = x + 2

⇒ x - y + 2 = 0.

From figure,

CD is inclined at an angle of -45° (As measured clockwise).

Slope = tan (-45°) = -1.

By point-slope form,

⇒ y - y₁ = m(x - x₁)

⇒ y - 0 = -1[x - (-2)]

⇒ y = -[x + 2]

⇒ y = -x - 2

⇒ x + y + 2 = 0.

Hence, equation of lines are x - y + 2 = 0 and x + y + 2 = 0.