Find equation of a line perpendicular to the line with given equation

Algebra I: Find equation of a line perpendicular to the line with given equation

This is a free lesson from our course in Algebra I


	In this part of lesson you'll learn how to find the equation of a line perpendicular to a given line. In such cases, we need to remember that in case of perpendicular lines, the product of their slopes is -1. This gives us a way to find the slope of the required equation -- if the slope of given line is m₁, the slope of perpendicular line will be -1/ m₁. The steps we need to take are as follows: • calculate slope of the new line as described above. • extract other information provided, e.g. the y-intercept, a given point on that line etc. • find the equation of the new line by using the slope and the other information provided to us. (More text below video...)

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	(Continued from above) Two lines or planes (or a line and a plane), are considered perpendicular (or orthogonal) to each other if they form congruent adjacent angles (an L-shape). The term may be used as a noun or adjective. In a coordinate plane, perpendicular lines have opposite reciprocal slopes. E.g.: Write an equation of the line perpendicular to 4y - x = 20 and containing the point (2, -3). Solution: Rewrite the equation in slope-intercept form. y = .25x + 5 We know the slope of the perpendicular line is -4 because .25 * -4 = -1. (Notice that the slope of the perpendicular line is the re- ciprocal of the other line's slope.). Now plug the given point and the slope into a slope-intercept equation to find the y intercept. -3 = (-4)2 + b Solve for b. b = 5 Now, you have the information you need to write an equation for a line perpendicular to 4y - x = 20. The answer is the following equation: y = -4x + 5.

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