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?

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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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