Q7. - Algebra 1

Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

What type of line does not have a defined slope?

A horizontal

B parallel

C perpendicular

D vertical

Step-by-Step Solution

Answer

The line that does not have a defined slope is vertical line. Therefore, the option D is correct.

Step 1. Write the formula for the slope of a line.

The slope of the line is given by:

 

$m=\tan \theta$ Where $m$ is the slope of the line and $\theta$ is the angle which the line makes with the positive $x$-axis in anticlockwise direction.

Step 2. Determine which line does not have a defined slope.

The slope of the line is given by:

$m=\tan \theta$

If the line makes an angle of $90$ degree with the positive $x$-axis in anticlockwise direction that is if the line is vertical then the value of $\theta$ is 90.

If the value of $\theta$ is 90, then 

$\begin{array}{c}m=\tan \theta \\ =\tan \left(90°\right)\\ =\text{undefined}\end{array}$

That implies, if the line is vertical, then the slope of the line is undefined.

Therefore, the line that does not have a defined slope is vertical line. 

Therefore, the option D is correct.