SOLUTION: find an equation of a line that contains the point (3,-5) and is perpendicular to x=4/-3

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Question 653195: find an equation of a line that contains the point (3,-5) and is perpendicular to x=4/-3
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find an equation of a line that contains the point (3,-5) and is perpendicular to x=4/-3
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Any line perpendicular to x = 4/(-3) must be a horizontal line.
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The horizontal line thru (3,-5) is y = -5
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Cheers,
Stan H.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The equation of a line with a defined slope m can also be written as follows:
y+=+mx+%2B+b+
you are given x=4%2F-3=-4%2F3; means x%2B4%2F3=0...->.. y=0
you can writ it in y+=+mx+%2B+b+ form as
0=+x+%2B+4%2F3+
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of 1, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%281%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F1%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-1%2F1 Multiply the fractions.


So the perpendicular slope is -1



So now we know the slope of the unknown line is -1 (its the negative reciprocal of 1 from the line y=1%2Ax%2B1.33333333333333). Also since the unknown line goes through (3,-5), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y%2B5=-1%2A%28x-3%29 Plug in m=-1, x%5B1%5D=3, and y%5B1%5D=-5



y%2B5=-1%2Ax%2B%281%29%283%29 Distribute -1



y%2B5=-1%2Ax%2B3 Multiply



y=-1%2Ax%2B3-5Subtract -5 from both sides to isolate y

y=-1%2Ax-2 Combine like terms

So the equation of the line that is perpendicular to y=1%2Ax%2B1.33333333333333 and goes through (3,-5) is y=-1%2Ax-2


So here are the graphs of the equations y=1%2Ax%2B1.33333333333333 and y=-1%2Ax-2




graph of the given equation y=1%2Ax%2B1.33333333333333 (red) and graph of the line y=-1%2Ax-2(green) that is perpendicular to the given graph and goes through (3,-5)