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.

Algebra ->  Points-lines-and-rays -> 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.      Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
The unknown line will have the form:
+y+=+m%2Ax+%2B+b+
The constant +m+ is the slope of the line
The constant +b+ is the y-intercept
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Say you are given the point (3 , -2 )
Plug these x and y values into the
above equation
+-2+=+m%2A3+%2B+b+
+3m+=+-b+-+2+
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Now you can use the slope information
to find +m+ and that will give you +b+
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Suppose the slope of the line that is
perpendicular to your unknown line is
+m1+=+7+
Any line which is perpendicular to the
given line will have a slope
+m+=+-1%2F7+ ( the negative reciprocal )
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Now you can say
+3m+=+-b+-+2+
+3%2A%28-1%2F7%29+=+-b+-+2+
+3%2F7+=+b+%2B+2+
+b+=+3%2F7+-+2+
+b+=+3%2F7+-14%2F7++
+b+=+-11%2F7+
----------------
Now you can construct the equation:
+y+=+%28-1%2F7%29%2Ax+-+11%2F7+
check:
Does it go through ( 3.-2 ) ?
+-2+=+%28-1%2F7%29%2A3+-+11%2F7+
+-2+=+-3%2F7+-+11%2F7+
+-2+=+-14%2F7+
+-2+=+-2+
OK
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Here's a plot of the equation
and also an equation perpendicular to it
that goes through the origin ( +y+=+7x+ )
+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+6%2C+7x%2C+%28-1%2F7%29%2Ax+-+11%2F7+%29+