How to Find a Perpendicular Line


If a line intersects another line at a 90-degree angle, they are perpendicular. You may have to find a perpendicular line as a part of a high school or college algebra or geometry course. You also may have to deal with perpendicular lines if you work in a career field that relies heavily upon math skills. Some of these career fields include engineering, architecture and design. You can find a perpendicular line by following a simple mathematical process.

  • Write down the slope of the given line using the slope-intercept formula, y = mx + b. The term "m" is the slope. For instance, if you have the equation y = 3x + 5, the slope of the would be 3/1 or 3.

  • Write the reciprocal of the slope. The reciprocal is the value that can be multiplied by the original number to reach the answer 1. If you have a whole number, place this number in the denominator of a fraction with 1 as the numerator. In this example, the reciprocal of 3 is 1/3. If you have a fraction, simply flip the fraction to find the reciprocal.

  • Add a negative sign to the reciprocal. In this example, you would turn 1/3 into -1/3.

  • Graph the perpendicular line with the new negative reciprocal slope. In this case, the entire equation for a perpendicular line would be y = -1/3x + 5. The two lines would intersect at 5 on the y axis, since 5 is the value for the y-intercept. Then you could graph other points on the line using 5 as your starting point and falling 1 unit as you run 3 units to the right. Connect the graphed points with a line to show the finished product.


  • Photo Credit Polka Dot Images/Polka Dot/Getty Images
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