SOLUTION: Please help me answer this question: What is the equation of the line, g(x), that is perpendicular to f(x)=1/2x+2 and passes through (0,2)?

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Question 144187: Please help me answer this question:
What is the equation of the line, g(x), that is perpendicular to f(x)=1/2x+2 and passes through (0,2)?
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%281%2F2%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%282%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=-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=%281%2F2%29%2Ax%2B2). Also since the unknown line goes through (0,2), 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-2=-2%2A%28x-0%29 Plug in m=-2, x%5B1%5D=0, and y%5B1%5D=2



y-2=-2%2Ax%2B%282%29%280%29 Distribute -2



y-2=-2%2Ax-0 Multiply



y=-2%2Ax-0%2B2Add 2 to both sides to isolate y

y=-2%2Ax%2B2 Combine like terms

So the equation of the line that is perpendicular to y=%281%2F2%29%2Ax%2B2 and goes through (0,2) is y=-2%2Ax%2B2


So here are the graphs of the equations y=%281%2F2%29%2Ax%2B2 and y=-2%2Ax%2B2




graph of the given equation y=%281%2F2%29%2Ax%2B2 (red) and graph of the line y=-2%2Ax%2B2(green) that is perpendicular to the given graph and goes through (0,2)