By the meaning of equally inclined lines, we mean that the lines which make equal angles with both the coordinate axes.
The above diagram shows that PQ and RS are the two equally inclined lines.
From the above diagram it is clear that;
For PQ: Inclination θ = 45°,
Therefore, slope = tan 45° = 1.
For RS: 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:
From the above diagram it is clear that; there are two lines PQ and RS, equally inclined to the coordinate axes.
For line PQ: 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 RS: 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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