Question
If a line has a slope of \( -4 \), what is the slope of a line that is perpendicular to it?
Ask by Gross Fleming. in South Africa
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The slope of a line perpendicular to one with a slope of \( -4 \) is \( \frac{1}{4} \).
Solution
To find the slope of a line that is perpendicular to another line with a given slope, you can use the concept of **negative reciprocals**.
**Here's how it works:**
1. **Identify the slope of the original line.**
In this case, the original line has a slope of \( m = -4 \).
2. **Find the negative reciprocal of the original slope.**
The negative reciprocal of a number \( m \) is \( -\frac{1}{m} \).
Applying this to the given slope:
\[
\text{Negative reciprocal of } -4 = -\left(\frac{1}{-4}\right) = \frac{1}{4}
\]
**Therefore, the slope of the line that is perpendicular to a line with a slope of \( -4 \) is \( \frac{1}{4} \).**
## Quick Summary:
- **Original slope (\( m \))**: \( -4 \)
- **Perpendicular slope**: \( \frac{1}{4} \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
If a line has a slope of \( -4 \), the slope of a line that is perpendicular to it can be found by taking the negative reciprocal of the original slope. The negative reciprocal of \( -4 \) is \( \frac{1}{4} \). Therefore, the slope of the perpendicular line is \( \frac{1}{4} \). This concept is not only crucial in algebra but also comes in handy in various real-world scenarios, like architecture or engineering design, where creating perpendicular angles is essential for structural stability. Think of it as a dance; when one line leads with a negative slope, its perpendicular partner twirls gracefully into a positive slope!
