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How to Find the Equation of a Perpendicular Line Given an Equation and Point Download ArticleExplore this Article Steps Steps Other Sections Questions & Answers Video Related Articles References Co-authored by Grace Imson, MA
Last Updated: December 10, 2020
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This article was co-authored by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been viewed 174,555 times.
Equations of perpendicular lines are usually introduced in the beginning of geometry or algebra, and are the starting points of many mathematical concepts. Some students may find them complex, but with this guide, you can find perpendicular lines with ease!
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1 Identify the equation's slope. In this guide, the slope would be m in slope-intercept form (y=mx+b).[1]X Expert Source Grace Imson, MAMath Instructor, City College of San FranciscoExpert Interview The photo above identifies 2/3 as the slope. The slope does not have to be fraction; it can be a whole number.
2 Change the slope. To change the slope, you must convert the value into its opposite sign (positive to negative or negative to positive). Plus, it must be put into its reciprocal version. The order in which the conversion is done does not matter. Refer to the example above.
2/3 becomes -2/3. This makes the slope opposite.
-2/3 becomes -3/2. This makes the slope both opposite and reciprocal. Thus, the slope has been converted.
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3 Write the new equation in slope-intercept form. Replace the old slope with the new slope. Replace the y-intercept's value with a variable (b).
4 Plug in the point's x- and y-values. This will make the equation ready to be solved. Solving it will lead to the y-intercept's value being found.[2]X Expert Source Grace Imson, MAMath Instructor, City College of San FranciscoExpert Interview
5 Solve the equation. Multiply the new slope with the x-value. Then, cancel out the product (make it become 0) with either addition or subtraction. Don't forget to add or subtract the y-value too. In the end, you should get the y-intercept.
6 Write the perpendicular line's equation. Still using slope-intercept form, use the new slope and the new y-intercept's value. This is the final answer.
7 (Optional) Check whether or not your answer is correct. Graph the two equations and measure one of the angles that forms; according to the definition of a perpendicular line, all four angles have to measure 90 degrees.
If the lines are horizontal and vertical, then they are perpendicular due to the "squares" of the coordinate grid.
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Question How do I find the perpendicular bisector between two points? Donagan Top Answerer See Find the Perpendicular Bisector of Two Points. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 8 Helpful 17
Question How do you find a perpendicular slope when the slope given is negative. For example, if asked: What is the slope of a line perpendicular to -4/5?" What would my answer be? Community Answer You use the negative reciprocal, in this case +5/4. Thanks! We're glad this was helpful.Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 0 Helpful 2
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↑ Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview
↑ Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview
About This Article
Co-authored by: Grace Imson, MA Math Instructor, City College of San Francisco This article was co-authored by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been viewed 174,555 times. 48 votes - 80% Co-authors: 9Updated: December 10, 2020 Views: 174,555 Categories: Coordinate Geometry In other languagesJapanese
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Yes No Advertisement Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy. Co-authored by: Grace Imson, MA Math Instructor, City College of San Francisco Co-authors: 9Updated: December 10, 2020 Views: 174,55580% of readers found this article helpful. 48 votes - 80% Click a star to add your vote
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Download Article Explore this Article Steps Steps Other Sections Questions & Answers Video Related Articles References Co-authored by Grace Imson, MA 
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Co-authored by: Grace Imson, MA Math Instructor, City College of San Francisco This article was co-authored by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been viewed 174,555 times. 48 votes - 80% Co-authors: 9 Updated: December 10, 2020 Views: 174,555 Categories: Coordinate Geometry In other languagesJapanese 
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493 
1 Identify the equation's slope. In this guide, the slope would be m in slope-intercept form (y=mx+b).[1] The photo above identifies 2/3 as the slope. The slope does not have to be fraction; it can be a whole number. 
2 Change the slope. To change the slope, you must convert the value into its opposite sign (positive to negative or negative to positive). Plus, it must be put into its reciprocal version. The order in which the conversion is done does not matter. Refer to the example above. 
3 Write the new equation in slope-intercept form. Replace the old slope with the new slope. Replace the y-intercept's value with a variable (b). 
4 Plug in the point's x- and y-values. This will make the equation ready to be solved. Solving it will lead to the y-intercept's value being found.[2] 
5 Solve the equation. Multiply the new slope with the x-value. Then, cancel out the product (make it become 0) with either addition or subtraction. Don't forget to add or subtract the y-value too. In the end, you should get the y-intercept. 
6 Write the perpendicular line's equation. Still using slope-intercept form, use the new slope and the new y-intercept's value. This is the final answer. 
7 (Optional) Check whether or not your answer is correct. Graph the two equations and measure one of the angles that forms; according to the definition of a perpendicular line, all four angles have to measure 90 degrees. 
Donagan Top Answerer See Find the Perpendicular Bisector of Two Points. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 8 Helpful 17 
Community Answer You use the negative reciprocal, in this case +5/4. Thanks! We're glad this was helpful. Thank you for your feedback. If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow Yes No Not Helpful 0 Helpful 2