SOLUTION: Write the equation of the line that is perpendicular to 2x-y=7 and goes through the point (-8,7).

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Question 955046: Write the equation of the line that is perpendicular to 2x-y=7 and goes through the point (-8,7).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the line that is perpendicular to 2x-y=7=>2x-7=y
and goes through the point (-8,7)

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%282%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F2%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-7). Also since the unknown line goes through (-8,7), 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-7=%28-1%2F2%29%2A%28x%2B8%29 Plug in m=-1%2F2, x%5B1%5D=-8, and y%5B1%5D=7



y-7=%28-1%2F2%29%2Ax%2B%281%2F2%29%28-8%29 Distribute -1%2F2



y-7=%28-1%2F2%29%2Ax-8%2F2 Multiply



y=%28-1%2F2%29%2Ax-8%2F2%2B7Add 7 to both sides to isolate y

y=%28-1%2F2%29%2Ax-8%2F2%2B14%2F2 Make into equivalent fractions with equal denominators



y=%28-1%2F2%29%2Ax%2B6%2F2 Combine the fractions



y=%28-1%2F2%29%2Ax%2B3 Reduce any fractions

So the equation of the line that is perpendicular to y=2%2Ax-7 and goes through (-8,7) is y=%28-1%2F2%29%2Ax%2B3


So here are the graphs of the equations y=2%2Ax-7 and y=%28-1%2F2%29%2Ax%2B3




graph of the given equation y=2%2Ax-7 (red) and graph of the line y=%28-1%2F2%29%2Ax%2B3(green) that is perpendicular to the given graph and goes through (-8,7)