Perpendicular lines have _______ _______ slopes.

Perpendicular lines have negative reciprocal slopes, which means that if one line has a slope of 'm', the slope of the line that is perpendicular to it will be '-1/m'. This relationship arises from the geometric definition of perpendicularity, where the angle formed by the intersection of the two lines is 90 degrees.

For example, if one line has a slope of 2 (which can also be expressed as the fraction 2/1), the negative reciprocal of that would be -1/2. These opposing slopes ensure that the lines cross at a right angle, which is the essence of their perpendicular relationship.

Understanding this concept is crucial when analyzing relationships between lines in geometry, algebra, or calculus, as it allows for the correct identification of angles and relationships in diagrams and equations.