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Question
A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.
Solution
The line makes intercepts 3 and 3 on the co-ordinate axes.
∴ the line is passing through the points (3, 0) and (0, 3).
∴ slope of the line = m = `(3 - 0)/(0 - 3)`
= `3/(-3)`
= – 1
Let θ be the inclination of the line.
∴ slope of the line = m = tan θ
∴ tan θ = –1
= – tan 45°
= tan (180° – 45°) ...[∵ tan (180° – θ) = – tan θ]
∴ tan θ = tan 135°
∴ θ = 135°
Hence, the inclination of the line = 135°.
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