To determine the slope of a line that is perpendicular to another given line, you must first find the slope of the original line. Every line can be represented mathematically by the equation of a line in the form of y = mx + b, where m represents the slope and b represents the y-intercept.
If the slope of the original line is m, then the slope of the line that is perpendicular to it is given by the negative reciprocal. This means:
- If the original slope m is a positive number, the perpendicular slope will be a negative number, specifically -1/m.
- If the original slope m is a negative number, the perpendicular slope will be positive as well, given by -1/m.
For example, if the original slope of the line is 2, the slope of the line perpendicular to it would be:
-1/2.
Conversely, if the original slope is -3, then the slope of the perpendicular line would be:
1/3.
Keep in mind that if the slope of the original line is 0 (meaning it’s a horizontal line), the slope of the perpendicular line would be undefined (a vertical line), as vertical lines cannot have a defined slope. Similarly, if the slope of the original line is undefined (a vertical line), the slope of the perpendicular line would be 0 (a horizontal line).
In conclusion, to find the slope of a line that is perpendicular to another, simply take the slope of the original line, calculate its negative reciprocal, and you’ll have your answer!