SOLUTION: Write the equation of the line that passes through (6,2) and is perpendicular to the line 2y-3x=5

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Question 1044105: Write the equation of the line that passes through (6,2) and is perpendicular to the line 2y-3x=5
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the line that passes through (6,2) and is perpendicular to the line 2y-3x=5=>2y=3x%2B5=>y=%283%2F2%29x%2B5%2F2

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 3%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%283%2F2%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%282%2F3%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%2F3 Multiply the fractions.


So the perpendicular slope is -2%2F3



So now we know the slope of the unknown line is -2%2F3 (its the negative reciprocal of 3%2F2 from the line y=%283%2F2%29%2Ax%2B5%2F2). Also since the unknown line goes through (6,2), 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=%28-2%2F3%29%2A%28x-6%29 Plug in m=-2%2F3, x%5B1%5D=6, and y%5B1%5D=2



y-2=%28-2%2F3%29%2Ax%2B%282%2F3%29%286%29 Distribute -2%2F3



y-2=%28-2%2F3%29%2Ax%2B12%2F3 Multiply



y=%28-2%2F3%29%2Ax%2B12%2F3%2B2Add 2 to both sides to isolate y

y=%28-2%2F3%29%2Ax%2B12%2F3%2B6%2F3 Make into equivalent fractions with equal denominators



y=%28-2%2F3%29%2Ax%2B18%2F3 Combine the fractions



y=%28-2%2F3%29%2Ax%2B6 Reduce any fractions

So the equation of the line that is perpendicular to y=%283%2F2%29%2Ax%2B5%2F2 and goes through (6,2) is y=%28-2%2F3%29%2Ax%2B6


So here are the graphs of the equations y=%283%2F2%29%2Ax%2B5%2F2 and y=%28-2%2F3%29%2Ax%2B6




graph of the given equation y=%283%2F2%29%2Ax%2B5%2F2 (red) and graph of the line y=%28-2%2F3%29%2Ax%2B6(green) that is perpendicular to the given graph and goes through (6,2)