Question

The slope of the line which makes \(\frac {3\pi}{4}\)angle with the positive direction of x-axis is

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

The Correct Option is A

To solve the problem, we need to find the slope of a line that makes an angle of $ \frac{3\pi}{4} $ with the positive direction of the x-axis.

1. Understanding the Relationship Between Slope and Angle:
The slope $m$ of a line is given by:

$ m = \tan(\theta) $
where $ \theta $ is the angle the line makes with the positive x-axis.

2. Substituting the Given Angle:
Here, $ \theta = \frac{3\pi}{4} $

So,
$ m = \tan\left(\frac{3\pi}{4}\right) $

3. Evaluating the Tangent:
We know that:
$ \tan\left(\frac{3\pi}{4}\right) = \tan\left(\pi - \frac{\pi}{4}\right) = -\tan\left(\frac{\pi}{4}\right) $
and $ \tan\left(\frac{\pi}{4}\right) = 1 $
Therefore,
$ m = -1 $

Final Answer:
The slope of the line is $ {-1} $.