SOLUTION: Please Help!!! "Find an equation for the line satisfying the given conditions. through (0,-8) and perpendicular to 20x+4y=41

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Question 906673: Please Help!!! "Find an equation for the line satisfying the given conditions. through (0,-8) and perpendicular to 20x+4y=41
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

through (0,-8) and perpendicular to 20x%2B4y=41
4y=-20x%2B41
y=-20x%2F4%2B41%2F4
y=+-5x%2B10.25
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 -5, 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%28-5%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-5%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=1%2F5 Multiply the fractions.


So the perpendicular slope is 1%2F5



So now we know the slope of the unknown line is 1%2F5 (its the negative reciprocal of -5 from the line y=-5%2Ax%2B10.25). Also since the unknown line goes through (0,-8), 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%2B8=%281%2F5%29%2A%28x-0%29 Plug in m=1%2F5, x%5B1%5D=0, and y%5B1%5D=-8



y%2B8=%281%2F5%29%2Ax-%281%2F5%29%280%29 Distribute 1%2F5



y%2B8=%281%2F5%29%2Ax-0%2F5 Multiply



y=%281%2F5%29%2Ax-0%2F5-8Subtract -8 from both sides to isolate y

y=%281%2F5%29%2Ax-0%2F5-40%2F5 Make into equivalent fractions with equal denominators



y=%281%2F5%29%2Ax-40%2F5 Combine the fractions



y=%281%2F5%29%2Ax-8 Reduce any fractions

So the equation of the line that is perpendicular to y=-5%2Ax%2B10.25 and goes through (0,-8) is y=%281%2F5%29%2Ax-8


So here are the graphs of the equations y=-5%2Ax%2B10.25 and y=%281%2F5%29%2Ax-8




graph of the given equation y=-5%2Ax%2B10.25 (red) and graph of the line y=%281%2F5%29%2Ax-8(green) that is perpendicular to the given graph and goes through (0,-8)





better graph:

+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+-5x%2B10.25%2C+%281%2F5%29x-8%29+