Can two lines with positive slope be perpendicular?

Expert Answers
lemjay eNotes educator| Certified Educator

Take note that two lines are perpendicular if their product of theirs slopes is -1.

`m_1*m_2 = -1`

So when we have two positive slopes, their product will be positive. Therefore,  when two lines have positive slopes, they are not perpendicular.

chrisyhsun | Student

I see in that a previous answer has already addressed the fact that for two lines to be perpendicular, the product of their slopes must equal -1. Since there is no way for two positive numbers to multiply to become -1, the scenario you stated is not an option. I also wanted to describe why this cannot be the case visually.


In the xy-plane, lines with positive slopes run from lower left to upper right (regardless of how steep the line is, they all follow this same pattern). However, in order for two lines to be perpendicular, they must be oriented completely differently. Since all the lines with positive slopes have essentially the same orientation, the scenario you asked about is invalid.

aishukul | Student

Two lines with positive slopes cannot be perpendicular. This is proven by this fact:

Slope of first line times slope of second line = -1. The product of the slopes of perpendicular lines has to be -1.

Also for a line to be positive, it has to have a positive slope. Likewise, negative line has to have negative slope. So, If two lines are positive, they would have positive slopes. And the product of the two slopes would result in a positive answer. But, for the lines to be perpendicular, the product of the slopes must equal -1. Therefore, one of the lines has to have a negative slope. Thus, two lines with positive slopes CANNOT be perpendicular.

kenkang | Student

If the axis are considered as positive , then you can say Yes.. since Y and X axis are perpendicular and they do not have negative slope.

carli1234 | Student

no, beccause a perpendicular line have slopes that are opposite recipricals of each other.