Question

What can be said regarding a line if its slope is negative?

• A. \( \theta \) is an obtuse angle
• B. \( \theta \) is equal to zero
• C. Either the line is the \( x \)-axis or it is parallel to the \( x \)-axis
• D. \( \theta \) is an acute angle

Hint:

When the slope of a line is negative, the angle it forms with the positive direction of the \( x \)-axis is between \( 90^\circ \) and \( 180^\circ \), which corresponds to an obtuse angle.

Answer 1

The Correct Option is A

The slope \( m \) of a line is related to the angle \( \theta \) it makes with the positive direction of the \( x \)-axis by the formula: \[ m = \tan \theta \] If the slope of the line is negative, then the tangent of the angle \( \theta \) is negative. The tangent function is negative in the second quadrant, where angles are between \( 90^\circ \) and \( 180^\circ \), i.e., the angle is obtuse. Thus, if the slope is negative, the angle \( \theta \) is obtuse. Therefore, the correct answer is \( \boxed{A} \).