SOLUTION: find the equation of the line that is perpendicular to y= -3/5x+2 and passes through point ( -4,2)

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Question 122254: find the equation of the line that is perpendicular to y= -3/5x+2 and passes through point ( -4,2)
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 -3%2F5, 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%28-3%2F5%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%285%2F-3%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=5%2F3 Multiply the fractions.


So the perpendicular slope is 5%2F3



So now we know the slope of the unknown line is 5%2F3 (its the negative reciprocal of -3%2F5 from the line y=%28-3%2F5%29%2Ax%2B2). Also since the unknown line goes through (-4,2), 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=%285%2F3%29%2A%28x%2B4%29 Plug in m=5%2F3, x%5B1%5D=-4, and y%5B1%5D=2



y-2=%285%2F3%29%2Ax-%285%2F3%29%28-4%29 Distribute 5%2F3



y-2=%285%2F3%29%2Ax%2B20%2F3 Multiply



y=%285%2F3%29%2Ax%2B20%2F3%2B2Add 2 to both sides to isolate y

y=%285%2F3%29%2Ax%2B20%2F3%2B6%2F3 Make into equivalent fractions with equal denominators



y=%285%2F3%29%2Ax%2B26%2F3 Combine the fractions



y=%285%2F3%29%2Ax%2B26%2F3 Reduce any fractions

So the equation of the line that is perpendicular to y=%28-3%2F5%29%2Ax%2B2 and goes through (-4,2) is y=%285%2F3%29%2Ax%2B26%2F3


So here are the graphs of the equations y=%28-3%2F5%29%2Ax%2B2 and y=%285%2F3%29%2Ax%2B26%2F3




graph of the given equation y=%28-3%2F5%29%2Ax%2B2 (red) and graph of the line y=%285%2F3%29%2Ax%2B26%2F3(green) that is perpendicular to the given graph and goes through (-4,2)