Equally inclined lines mean: the lines which make equal angles with both the coordinate axes.
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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 coordinate axes.
Solution:
As is clear from the diagram, there are two lines AB and CD, equally inclined to the coordinate 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
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