How to find the slope of a perpendicular line?
Understand the Problem
The question is asking how to calculate the slope of a line that is perpendicular to another line. To find this, we need to understand that if we have the slope of one line, the slope of a perpendicular line can be determined using the negative reciprocal of the original slope.
Answer
-\frac{1}{m}
Answer for screen readers
The slope of the perpendicular line is the negative reciprocal of the original slope, $-\frac{1}{m}$.
Steps to Solve
- Identify the slope of the given line
First, find the slope of the original line. The slope is often represented by $m$ and can be found if the equation of the line is given in the slope-intercept form $y = mx + b$. If the line equation is in a different form, you may need to convert it first.
- Find the negative reciprocal of the slope
The slope of a line perpendicular to the original line is the negative reciprocal of the original slope $m$. This means if the slope of the original line is $m$, then the slope $m'$ of the perpendicular line is $-\frac{1}{m}$.
- Combine the results
State the final result clearly after calculating the negative reciprocal.
The slope of the perpendicular line is the negative reciprocal of the original slope, $-\frac{1}{m}$.
More Information
If the slope of the original line is positive, the slope of the perpendicular line is negative, and vice versa. This is because perpendicular lines intersect at right angles, creating a consistent relationship between their slopes.
Tips
Common mistakes include forgetting to take the reciprocal of the original slope or forgetting to change the sign. Always double-check your work to ensure the negative reciprocal is correctly calculated.