What is the relationship between the slopes of two perpendicular lines?

The relationship between the slopes of two perpendicular lines is that they are opposite reciprocals of each other. When two lines are perpendicular, the product of their slopes is equal to -1. This means that if the slope of one line is represented as (m), the slope of the line that is perpendicular to it can be expressed as (-\frac{1}{m}).

For example, if one line has a slope of 2, the slope of the line that is perpendicular to it would be (-\frac{1}{2}). This negative sign indicates that the lines cross at a right angle, and the fact that they are reciprocals reflects the way their angles relate to each other. Thus, the correct choice emphasizes that the slopes not only differ in their sign but also are inversely proportional to each other, leading to the conclusion that they are opposite reciprocals.

To reinforce the understanding, it is useful to clarify that simply being equal or the same would not meet the definition of perpendicular lines, as those lines would overlap rather than intersect at a right angle.