Part 3/5:
When the line ( Y = 2X ) is graphed, it creates an upward slope. Conversely, the line with the negative reciprocal slope, ( Y = -\frac{1}{2}X ), will yield a downward slope. Graphically, when these two lines are represented, they intersect at a right angle, demonstrating the perpendicular nature of these slopes.
Establishing the Proof of Perpendicularity
To formally prove that two lines are perpendicular, we consider a line expressed as:
[ Y = \frac{A}{B}X ]
In this equation, ( A ) is the rise and ( B ) is the run, defining the slope.
Now, consider the negative reciprocal, expressed as:
[ Y = -\frac{B}{A}X ]