By the meaning of equally inclined lines, we mean that the lines which make equal angles with both the co-ordinate 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 co-ordinate axes.
Solution:
From the above diagram it is clear that; there are two lines PQ and RS, equally inclined to the co-ordinate 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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