SOLUTION: write an equation of the line containing the given point and perpendicular to the given line (4,-6); 8x+5y=2

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Question 911279: write an equation of the line containing the given point and perpendicular to the given line (4,-6); 8x+5y=2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the given line 8x%2B5y=2
=> 5y=-8x%2B2
=> y=-%288%2F5%29x%2B2%2F5
and point (4,-6)

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 -8%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%28-8%2F5%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%285%2F-8%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%2F8 Multiply the fractions.


So the perpendicular slope is 5%2F8



So now we know the slope of the unknown line is 5%2F8 (its the negative reciprocal of -8%2F5 from the line y=%28-8%2F5%29%2Ax%2B2%2F5). Also since the unknown line goes through (4,-6), 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%2B6=%285%2F8%29%2A%28x-4%29 Plug in m=5%2F8, x%5B1%5D=4, and y%5B1%5D=-6



y%2B6=%285%2F8%29%2Ax-%285%2F8%29%284%29 Distribute 5%2F8



y%2B6=%285%2F8%29%2Ax-20%2F8 Multiply



y=%285%2F8%29%2Ax-20%2F8-6Subtract -6 from both sides to isolate y

y=%285%2F8%29%2Ax-20%2F8-48%2F8 Make into equivalent fractions with equal denominators



y=%285%2F8%29%2Ax-68%2F8 Combine the fractions



y=%285%2F8%29%2Ax-17%2F2 Reduce any fractions

So the equation of the line that is perpendicular to y=%28-8%2F5%29%2Ax%2B2%2F5 and goes through (4,-6) is y=%285%2F8%29%2Ax-17%2F2


So here are the graphs of the equations y=%28-8%2F5%29%2Ax%2B2%2F5 and y=%285%2F8%29%2Ax-17%2F2




graph of the given equation y=%28-8%2F5%29%2Ax%2B2%2F5 (red) and graph of the line y=%285%2F8%29%2Ax-17%2F2(green) that is perpendicular to the given graph and goes through (4,-6)