The slope of a given line is 5 . What is the slope of a line parallel to the given line? What is the slope of a line perpendicular to the given line?

To determine the slopes of lines that are either **parallel** or **perpendicular** to a given line with a slope of **5**, let's review some key concepts in geometry. ### 1. Slope of a Parallel Line **Parallel lines** have the **same slope**. This means that any line parallel to the given line will also have a slope of **5**. - **Slope of a parallel line:** **5** ### 2. Slope of a Perpendicular Line **Perpendicular lines** have slopes that are **negative reciprocals** of each other. To find the negative reciprocal of the given slope: 1. **Reciprocal of 5:** Since the slope is 5, its reciprocal is \( \frac{1}{5} \). 2. **Negative Reciprocal:** Change the sign of the reciprocal, resulting in \( -\frac{1}{5} \). - **Slope of a perpendicular line:** **\(-\frac{1}{5}\)** ### **Summary** - **Parallel Line Slope:** 5 - **Perpendicular Line Slope:** \(-\frac{1}{5}\) Understanding these relationships is fundamental in geometry, especially when analyzing the orientations of different lines relative to one another.