SOLUTION: consider l: 2x+y+4=0 find the equation of a line perpendicular to l passing through the points 5,3 give your answer in the form ax+by+c=0

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Question 890802: consider l: 2x+y+4=0
find the equation of a line perpendicular to l passing through the points 5,3 give your answer in the form ax+by+c=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2By%2B4=0
the point 5%2C3
2x%2By%2B4=0 =>y=-2x-4
the equation of a line perpendicular is
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 -2, 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%28-2%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-2%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%2F2 Multiply the fractions.


So the perpendicular slope is 1%2F2



So now we know the slope of the unknown line is 1%2F2 (its the negative reciprocal of -2 from the line y=-2%2Ax-4). Also since the unknown line goes through (5,3), 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-3=%281%2F2%29%2A%28x-5%29 Plug in m=1%2F2, x%5B1%5D=5, and y%5B1%5D=3



y-3=%281%2F2%29%2Ax-%281%2F2%29%285%29 Distribute 1%2F2



y-3=%281%2F2%29%2Ax-5%2F2 Multiply



y=%281%2F2%29%2Ax-5%2F2%2B3Add 3 to both sides to isolate y

y=%281%2F2%29%2Ax-5%2F2%2B6%2F2 Make into equivalent fractions with equal denominators



y=%281%2F2%29%2Ax%2B1%2F2 Combine the fractions



y=%281%2F2%29%2Ax%2B1%2F2 Reduce any fractions

So the equation of the line that is perpendicular to y=-2%2Ax-4 and goes through (5,3) is y=%281%2F2%29%2Ax%2B1%2F2


So here are the graphs of the equations y=-2%2Ax-4 and y=%281%2F2%29%2Ax%2B1%2F2




graph of the given equation y=-2%2Ax-4 (red) and graph of the line y=%281%2F2%29%2Ax%2B1%2F2(green) that is perpendicular to the given graph and goes through (5,3)





=>y=%281%2F2%29x%2B1%2F2 in the form ax%2Bby%2Bc=0 will
be -%281%2F2%29x%2By-1%2F2=0 or multiply all by 2 and you have =>-x%2B2y-1=0

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x%2B1%2F2%2C+-2x-4%29+