Perpendicular lines are special because their slopes multiply to -1. This happens because they are opposites and reciprocals of each other.

Understanding the Concept:

1. Slope of a Line: The slope tells us how steep a line is. In the equation $y = mx + b$, the letter $m$ is the slope.

2. Reciprocal: The reciprocal of a number $a$ is found by flipping it. For example, the reciprocal of 4 is $\frac{1}{4}$.

3. Opposite: The opposite of a number changes its sign. For instance, the opposite of 5 is -5.

Example:

• Line 1: The equation $y = 2x + 3$ has a slope of $m_1 = 2$.

• Line 2: A line that is perpendicular to the first one will have a slope of $m_2 = -\frac{1}{2}$.

Calculation:

Let’s multiply the slopes of these lines:

$m_1 \times m_2 = 2 \times -\frac{1}{2} = -1$

This important rule helps us when we draw graphs or solve problems in geometry. It makes sure that whenever lines cross each other, the angles they form are right angles!