Question

Eric states that the slopes of perpendicular lines are opposite reciprocals (i.e. that the slope of one is equal to the negative of the reciprocal of the other), and Aviva states that the product of the slopes of perpendicular lines is −1. Who is correct? Why? Explain your reasoning with an example. If one of the lines is vertical and the other one is horizontal, how would your answer change?

Answer 1

Eric's statement is correct that the slopes of the perpendicular lines are opposites reciprocal with each other compared to Aviva's. Aviva's statement is correct but is not usually the case. An example is that when you are given these functions such as y = -2x + 3 and y = 1/2x + 4. The coefficients of the x variable are 2 and negative 1/2. The slopes must be in opposite signs so that the two functions will intersect at a common point and will form a ninety degree angle. This is the very basis of a perpendicular line because if both lines have the same slopes, then both lines are just parallel with each other, they cannot intersect.