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Question 1036296: Find the slope of a line parallel and perpendicular to the given line.
y=-8/7x+1
Answer by aditya2117(32)   (Show Source):
You can put this solution on YOUR website! The slope here is m=-8/7 . Let the slope of the given line be 'p'.
1) If we want it to be parallel then their slopes must be equal , i.e. m=p=-8/7.
The equation of the line will differ by an constant ,
y = -8x/7 + C (where C is the arbitary constant)
2) If we want it to be perpendicular we must have them inclined at 90 degress.
We know for this condition we must have mp=-1, Still let us derive it.
The angles formed by the lines with the positive x-axis are a & b respectively
where tan(a)=m,tan(b)=p.
we must have, b - a = 90
or, arctan(p)-arctan(m)=90
or, arctan(p-m/1+pm)=arctan(infinity)
So for (p-m)/(1+pm) to be infinity we must have denominator zero i.e. mp=-1.
Now the slope p=8/7 and thus the equation is : y = 8x/7 + K (where K is arbitary constant)
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