Question

The slopes of the two line segments are equal. Which of the following is correct?
A) The line segments are parallel.
B) The end points of the line segments are collinear.
C) The line segments are perpendicular.
D) The end points of the line segments are non-collinear.

Answer 1

Hint: The slope is a measure of the angle of a line from the horizontal. It is the measure of steepness and direction of a straight line. If the angle of inclination of a line with the x-axis is $\theta $, then the slope of the line is given by $m = \tan \theta $.

Complete step-by-step answer:
Consider two parallel lines given by ${l_1}$ and ${l_2}$ with inclinations $\alpha $ and $\beta $ respectively. For two lines to be parallel, their inclination must be equal i.e., $\alpha = \beta $ . This results in the fact that $\tan \alpha = \tan \beta $.Therefore, if two lines are parallel then ${m_1} = {m_2}$.
Thus, if the slopes of two lines on the Cartesian plane are equal, then the lines are parallel to each other.

Thus, if the slopes of two lines on the Cartesian plane are equal, then the lines are parallel to each other.

Hence, option (A) is the correct answer.

Note: The angle of inclination $\left( \theta \right)$ is the angle which a line makes with the positive direction of x-axis. $\theta $ lies between $0^\circ $ and $180^\circ $.