Question
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?
Ask by Knight Zimmerman. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
A line parallel to the given line has a slope of 5, and a perpendicular line has a slope of -1/5.
Solution
To solve the problem, we need to understand the properties of slopes in relation to parallel and perpendicular lines.
1. **Slope of a Parallel Line:**
- Lines that are parallel have the same slope. Therefore, if the slope of the given line is \( m = 5 \), the slope of a line parallel to it will also be \( m = 5 \).
2. **Slope of a Perpendicular Line:**
- The slope of a line that is perpendicular to another line is the negative reciprocal of the slope of the original line. The negative reciprocal of a slope \( m \) is given by \( -\frac{1}{m} \).
- For the given line with a slope of \( m = 5 \), the slope of a line perpendicular to it will be:
\[
m_{\text{perpendicular}} = -\frac{1}{5}
\]
### Summary:
- The slope of a line parallel to the given line is \( 5 \).
- The slope of a line perpendicular to the given line is \( -\frac{1}{5} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
If a line has a slope of 5, any line parallel to it will also have a slope of 5. This is because parallel lines share the same steepness and direction, so you're in good shape whenever you're working with lines that run side by side! Now, for perpendicular lines, things get a bit more interesting! The slope of a line that is perpendicular to the given line can be found by taking the negative reciprocal of the original slope. So, since the original slope is 5, the perpendicular slope would be -1/5. This means that while one line is climbing steeply, the other is headed down in a more gentle manner—talk about a perfect pair!
