SOLUTION: Find the equation of the line. Write the equation using function notation. Through (8, -1) and perpendicular to 8y=x-16

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Question 925425: Find the equation of the line. Write the equation using function notation.
Through (8, -1) and perpendicular to 8y=x-16

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
through (8,+-1) and perpendicular to 8y=x-16
8y=x-16
y=x%2F8-16%2F8
y=%281%2F8%29x-2

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%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%281%2F8%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%288%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=-8%2F1 Multiply the fractions.


So the perpendicular slope is -8



So now we know the slope of the unknown line is -8 (its the negative reciprocal of 1%2F8 from the line y=%281%2F8%29%2Ax-2). Also since the unknown line goes through (8,-1), 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%2B1=-8%2A%28x-8%29 Plug in m=-8, x%5B1%5D=8, and y%5B1%5D=-1



y%2B1=-8%2Ax%2B%288%29%288%29 Distribute -8



y%2B1=-8%2Ax%2B64 Multiply



y=-8%2Ax%2B64-1Subtract -1 from both sides to isolate y

y=-8%2Ax%2B63 Combine like terms

So the equation of the line that is perpendicular to y=%281%2F8%29%2Ax-2 and goes through (8,-1) is y=-8%2Ax%2B63


So here are the graphs of the equations y=%281%2F8%29%2Ax-2 and y=-8%2Ax%2B63




graph of the given equation y=%281%2F8%29%2Ax-2 (red) and graph of the line y=-8%2Ax%2B63(green) that is perpendicular to the given graph and goes through (8,-1)