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...)
(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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