Question

If line p has a slope of zero, and line m has an undefined slope, what can you conclude about line p and line m?

A. Line p is a vertical line and line m is a horizontal line, therefore the two lines are perpendicular.
B. Line p is a horizontal line and line m is a vertical line, therefore the two lines are perpendicular.
C. Line p and line m are both vertical lines, therefore the two lines are parallel.
D. Line p and line m are both horizontal lines, therefore the two lines are parallel.

Answer 1

A line with a slope of zero is horizontal, and a line with an undefined slope is vertical. Because one is horizontal and the other is vertical, these lines are perpendicular to each other.

Step-by-step explanation:

If line p has a slope of zero, it means that it is a horizontal line, as it does not rise or fall but remains constant on the y-axis. On the other hand, a line with an undefined slope, such as line m, is a vertical line because there is a change on the y-axis but no change on the x-axis, which would equate to a division by zero in the slope formula, hence undefined. Consequently, with line p being horizontal and line m being vertical, we can conclude that the two lines are perpendicular to each other. Therefore, the correct answer is B: Line p is a horizontal line and line m is a vertical line, therefore the two lines are perpendicular.