Determine whether each statement is always, sometimes, or never true. Explain.

Question

1. Two lines with different slopes are perpendicular.

 

 

2. The slopes of vertical lines and horizontal lines are negative reciprocals.

 

 

3. A vertical line is perpendicular to the x-axis.

Answer 1

Hi Aim, the answers are:

 

1. Sometimes. Just because the slopes are different, does not make them perpendicular. For the two lines to be perpendicular, the two slopes must be negative reciprocals of each other. 

 

It is possible two lines are perpendicular, therefore the answers of always and never are not true.

 

2. Never. The slope of a vertical line is undefined. The slope of a horizontal line is 0. It is not possible for one to be the negative reciprocal of the other.

 

3. Always. By definition, the x-axis is the horizontal axis. Therefore, a vertical line is perpendicular to the x-axis.

 

Questions?