Question

Find the slope of a line perpendicular to each given line.
What does a perpendicular slope look like?

Answer 1

To find the slope of a line that is perpendicular to a given line, you need to understand the relationship between the slopes of perpendicular lines.

1. **Identifying the slope of the given line**: If you have a line expressed in the slope-intercept form, \( y = mx + b \), where \( m \) is the slope, then the slope of the given line is \( m \).

2. **Finding the perpendicular slope**: The slope of a line that is perpendicular to another line is the negative reciprocal of the original slope. This means you follow these steps:
- If the slope of the original line is \( m \), then the slope of the perpendicular line \( m_\perp \) is given by:
\[
m_\perp = -\frac{1}{m}
\]
- If the original slope \( m = 0 \) (horizontal line), the perpendicular slope will be undefined (vertical line).
- If the original slope \( m \) is undefined (vertical line), the perpendicular slope will be 0 (horizontal line).

### Example
- If the slope of the given line is \( m = 2 \):
\[
m_\perp = -\frac{1}{2}
\]

- If the slope of the given line is \( m = -3 \):
\[
m_\perp = \frac{1}{3}
\]

- If the line is vertical (undefined slope), the perpendicular slope will be 0 (horizontal line).

### Graphical Representation
- Perpendicular slopes visually represent as two lines crossing at a right angle (90 degrees).

### Summary
- To find a perpendicular slope, take the negative reciprocal of the original line's slope.
- The relationship between the slopes of lines is crucial for solving geometry problems involving perpendicular lines.