Lane Peterson
12/12/2023 · Junior High School
Consider the line \( y=-\frac{5}{4} x-\frac{1}{5} \) What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?
UpStudy ThothAI Solution
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Step-by-step Solution
The given line is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope. For the line \( y = -\frac{5}{4} x - \frac{1}{5} \), the slope \( m \) is \( -\frac{5}{4} \).
1. **Slope of a line perpendicular to this line:**
The slope of a line that is perpendicular to another line is the negative reciprocal of the slope of the original line.
The slope of the given line is \( -\frac{5}{4} \). The negative reciprocal is calculated as follows:
\[
\text{Perpendicular slope} = -\frac{1}{-\frac{5}{4}} = \frac{4}{5}
\]
2. **Slope of a line parallel to this line:**
The slope of a line that is parallel to another line is the same as the slope of the original line.
Therefore, the slope of a line parallel to the given line is:
\[
\text{Parallel slope} = -\frac{5}{4}
\]
In summary:
- The slope of a line perpendicular to the given line is \( \frac{4}{5} \).
- The slope of a line parallel to the given line is \( -\frac{5}{4} \).
Quick Answer
The slope of a line perpendicular to the given line is \( \frac{4}{5} \), and the slope of a line parallel to the given line is \( -\frac{5}{4} \).
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