SOLUTION: Write an equation for the line that goes through point (2,-1) and is perpendicular to the line, y=-1/2x+3

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Question 132452: Write an equation for the line that goes through point (2,-1) and is perpendicular to the line, y=-1/2x+3
Answer by jim_thompson5910(35256) 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%2F2, 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%28-1%2F2%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%282%2F-1%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



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


So the perpendicular slope is 2



So now we know the slope of the unknown line is 2 (its the negative reciprocal of -1%2F2 from the line y=%28-1%2F2%29%2Ax%2B3). Also since the unknown line goes through (2,-1), 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%2B1=2%2A%28x-2%29 Plug in m=2, x%5B1%5D=2, and y%5B1%5D=-1



y%2B1=2%2Ax-%282%29%282%29 Distribute 2



y%2B1=2%2Ax-4 Multiply



y=2%2Ax-4-1Subtract -1 from both sides to isolate y

y=2%2Ax-5 Combine like terms

So the equation of the line that is perpendicular to y=%28-1%2F2%29%2Ax%2B3 and goes through (2,-1) is y=2%2Ax-5


So here are the graphs of the equations y=%28-1%2F2%29%2Ax%2B3 and y=2%2Ax-5




graph of the given equation y=%28-1%2F2%29%2Ax%2B3 (red) and graph of the line y=2%2Ax-5(green) that is perpendicular to the given graph and goes through (2,-1)