How do you find the negative reciprocal of a slope?

The concept of the negative reciprocal of a slope is essential in understanding the relationship between perpendicular lines in geometry. When two lines are perpendicular, the product of their slopes is -1. Therefore, to find the slope of a line that is perpendicular to a given slope, you take the negative reciprocal.

To find the negative reciprocal of a slope expressed as a fraction, you follow these steps:

1. Flip the fraction, which means you exchange the numerator and the denominator.

2. Change the sign, which means if the original slope is positive, the new slope will be negative, and vice versa.

For example, if the slope of a line is 2 (which can be written as 2/1), the negative reciprocal would be -1/2.

This process effectively gives you the correct slope for a line that is perpendicular to the original line, hence affirming why flipping the fraction and changing the sign is the method to use.