Part 2/5:
This relationship is vital when dealing with slopes of lines, especially in the context of geometry.
Exploring Negative Reciprocals with Line Equations
To illustrate how negative reciprocals work, consider a linear equation:
[ Y = 2X ]
The slope of this equation is 2, which can be visualized as a rise of 2 over a run of 1 (i.e., slope = rise/run = 2/1).
To find the negative reciprocal of the slope 2, we take the reciprocal of 2 (which is ( \frac{1}{2} )) and introduce the negative sign to get:
[ -\frac{1}{2} ]
This means that for any line that has a positive slope of 2, a line that has a slope of -1/2 will be perpendicular to it.