SOLUTION: What is the line that passes through (1, -5) and is perpendicular to a line with a slope of 1?

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Question 1104251: What is the line that passes through (1, -5) and is perpendicular to a line with a slope of 1?
Found 2 solutions by richwmiller, josgarithmetic:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B0). Also since the unknown line goes through (1,-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-1%29 Plug in m=-1, x%5B1%5D=1, and y%5B1%5D=-5



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



y%2B5=-1%2Ax%2B1 Multiply



y=-1%2Ax%2B1-5Subtract -5 from both sides to isolate y

y=-1%2Ax-4 Combine like terms

So the equation of the line that is perpendicular to y=1%2Ax%2B0 and goes through (1,-5) is y=-1%2Ax-4


So here are the graphs of the equations y=1%2Ax%2B0 and y=-1%2Ax-4




graph of the given equation y=1%2Ax%2B0 (red) and graph of the line y=-1%2Ax-4(green) that is perpendicular to the given graph and goes through (1,-5)

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
What is the line that passes through (1, -5) and is perpendicular to a line with a slope of 1?
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The perpendicular line wanted will have slope, -1.

%28y-%28-5%29%29%2F%28x-1%29=-1, using formula for slope

y%2B5=-1%28x-1%29
y=-x%2B1-5
highlight%28y=-x-4%29