SOLUTION: If you know a point on a line and you know the equation of a line perpendicular to this line, explain how to write the line's equation. Please provide an example of the line.

Question 808135: If you know a point on a line and you know the equation of a line perpendicular to this line, explain how to write the line's equation.
Please provide an example of the line.
Found 2 solutions by TimothyLamb, josmiceli:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
Perpendicular lines have negative reciprocal slopes
Given L1: y = 5x + 3
a line L2 perpendicular to L1 will have slope m = (-1/5)
Given point p=(x2,y2) on L2, use the point-slope form to write L2's equation
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y - y2 = (-1/5)(x - x2)
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The unknown line will have the form:

The constant is the slope of the line
The constant is the y-intercept
-------------
Say you are given the point (3 , -2 )
Plug these x and y values into the
above equation

----------------
Now you can use the slope information
to find and that will give you
----------------
Suppose the slope of the line that is
perpendicular to your unknown line is

Any line which is perpendicular to the
given line will have a slope
( the negative reciprocal )
-----------------
Now you can say

----------------
Now you can construct the equation:

check:
Does it go through ( 3.-2 ) ?

OK
----------------
Here's a plot of the equation
and also an equation perpendicular to it
that goes through the origin ( )

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