How to Find the Slope of Perpendicular Lines

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All lines on a graph have a slope, or the angle at which it rises or falls. Slope is found by using the units on a graph. A line can have either a positive or negative slope, meaning the line either continues upward into the positive number range or falls downward into the negative number range. Two lines that are perpendicular to each other both cross at the same point while one has a positive slope and the other has a negative slope.

Equation Format

  • Determine the slope of the first line by looking at the equation. A standard line equation is written as y = mx+b where the letter "m" is the slope, and "b" is the value of "y" where the lines will cross. If the equation is y = 5x-3, then the slope of the first line is 5.

  • Find the negative reciprocal of the slope of the first line by flipping the fraction and using the opposite sign. If the original slope is 5, the negative reciprocal is -1/5. This is the slope of the second line, the one perpendicular to the line in the equation.

  • Graph both lines to ensure you've done everything correctly. The first line, in the example above, will be: y = 5x-3, and the second will be: y = -1/5x-3. The lines should be perpendicular and cross on the graph where y = -3.

Graph Format

  • Find the rise and the run. If your line crosses through the origin, (0, 0) and the points (2, 1), then you will count to the right two and up one. The number of units you counted up is called rise. The number of units you counted over is called run.

  • Place the rise over the run in fraction format. This is your slope. In the above example, the slope is ½.

  • Find the negative reciprocal of the slope of the first line by flipping the fraction and using the opposite sign. If the original slope is 1/2, the negative reciprocal is -2. This is the slope of the second line.

  • Check your work by determining the slope of the second line using the rise over run method. You should come out with the same slope you found when you applied the negative reciprocal method. If the numbers don't match, you counted rise and run incorrectly or didn't apply the negative reciprocal method correctly.

Tips & Warnings

  • If one line is horizontal, it has a slope of zero. Its perpendicular line has a slope called "undefined" because there is no such number as -1/0, the negative reciprocal of 0/1.

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