Question

Determine the fraction for the perpendicular slope. The line m has a slope of a/b, where a and b are integers. What is the slope of a line that is perpendicular to line m?

A) a/b
B) b/a
C) -b/a
D) -b/a

Answer 1

The slope of a line perpendicular to a line with slope a/b is -b/a, because the slopes of perpendicular lines are negative reciprocals of each other.

Step-by-step explanation:

The slope m of a straight line is defined as the rise divided by the run. Given a line with a slope of a/b, an important concept in algebraic geometry is that the slope of a line perpendicular to this one is the negative reciprocal of a/b. Accordingly, if the slope of line m is a/b, the slope of a perpendicular line would be -b/a.

For example, if a line has a slope of 3 (a rise of 3 units for every 1 unit of run), a line perpendicular to it would have a slope of -1/3. This is because the product of the slopes of two perpendicular lines in a Cartesian plane is -1. Therefore, the correct answer to the given question is C) -b/a.