SOLUTION: What is the equation for the line is perpendicular to 7x + 8y = 2 and passes through (4,2).

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Question 946295: What is the equation for the line is perpendicular to 7x + 8y = 2 and passes through (4,2).
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Easiest way requires knowing how standard form equation for a line works.

The line perpendicular is 8x-7y=c, and just use the needed point on this line, 8x-7y=c, to find c.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the equation for the line is perpendicular to 7x+%2B+8y+=+2
and passes through (4,2)
8y+=-7x+%2B+2
y+=-%287%2F8%29x+%2B+2%2F8
y+=-%287%2F8%29x+%2B+1%2F4

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 -7%2F8, 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%28-7%2F8%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%288%2F-7%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=8%2F7 Multiply the fractions.


So the perpendicular slope is 8%2F7



So now we know the slope of the unknown line is 8%2F7 (its the negative reciprocal of -7%2F8 from the line y=%28-7%2F8%29%2Ax%2B1%2F4). 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=%288%2F7%29%2A%28x-4%29 Plug in m=8%2F7, x%5B1%5D=4, and y%5B1%5D=2



y-2=%288%2F7%29%2Ax-%288%2F7%29%284%29 Distribute 8%2F7



y-2=%288%2F7%29%2Ax-32%2F7 Multiply



y=%288%2F7%29%2Ax-32%2F7%2B2Add 2 to both sides to isolate y

y=%288%2F7%29%2Ax-32%2F7%2B14%2F7 Make into equivalent fractions with equal denominators



y=%288%2F7%29%2Ax-18%2F7 Combine the fractions



y=%288%2F7%29%2Ax-18%2F7 Reduce any fractions

So the equation of the line that is perpendicular to y=%28-7%2F8%29%2Ax%2B1%2F4 and goes through (4,2) is y=%288%2F7%29%2Ax-18%2F7


So here are the graphs of the equations y=%28-7%2F8%29%2Ax%2B1%2F4 and y=%288%2F7%29%2Ax-18%2F7




graph of the given equation y=%28-7%2F8%29%2Ax%2B1%2F4 (red) and graph of the line y=%288%2F7%29%2Ax-18%2F7(green) that is perpendicular to the given graph and goes through (4,2)