Find the slope of a line whose inclination with the positive x-axis is 135^°.

Worked Examples · Example 4

135^\circ

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By definition the slope of a line is $m = \tan\theta$ , where $\theta$ is the inclination of the line with the positive x-axis.

Here $\theta = 135^\circ$ . Since $135^\circ = 180^\circ - 45^\circ$ , and $\tan(180^\circ - \theta) = -\tan\theta$ :

$m = \tan 135^\circ = -\tan 45^\circ = -1$ …

Q.Find the slope of a line whose inclination with the positive x-axis is $135^\circ$ .