# Equally Inclined Lines

Equally inclined lines mean: the lines which make equal angles with both the co-ordinate axes.

PICCCCCCCCCCC
The above diagram shows two equally inclined lines AB and CD.

As is clear from the above diagram:

For AB: Inclination θ = 45°,

Therefore, slope = tan 45° = 1.

For CD: Inclination θ = -45°,

Therefore, slope = tan (-45°) = -1.

Solved example on equally inclined lines:

Find the equation of the lines which is passes through the point (-2. 3) and equally inclined to the co-ordinate axes.

Solution:

As is clear from the diagram, there are two lines AB and CD, equally inclined to the co-ordinate axes.

For line AB: m = tan 45° = 1

and (x$$_{1}$$, y$$_{1}$$) = (-2, 3)

Therefore, its equation: y – y$$_{1}$$ = m(x – x$$_{1}$$)

⟹ y – 3 = 1(x + 2)

⟹ y - 3 = x + 2

⟹ y = x + 5

For line CD: m = tan (-45°) = -1

and (x$$_{1}$$, y$$_{1}$$) = (-2, 3)

Therefore, its equation: y – y$$_{1}$$ = m(x – x$$_{1}$$)

⟹ y – 3 = -1(x + 2)

⟹ y - 3 = -x - 2

⟹ y = -x + 1

Therefore, the required equations are y = x + 5 and y = -x + 1