SOLUTION: perpendicular to -x + 5y = -6, y-intercept (0,-7)

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Question 762448: perpendicular to -x + 5y = -6, y-intercept (0,-7)
Found 2 solutions by Cromlix, MathLover1:
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Sort into y = mx + c
-x + 5y = -6
5y = x - 6
y = 1/5x - 6/5
Lines that are perpendicular
have gradients that multiply
together to give -1
m1 x m2 = -1
So, new gradient = -5
Using y = mx + c
y = -5x - 7.
Hope this helps
:-)

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
+-x+%2B+5y+=+-6,
y-intercept (0,-7)
+-x+%2B+5y+=+-6...solve for y
++5y+=+x-6
++y+=+%281%2F5%29x-6%2F5
++y+=+0.2x-1.2

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%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%281%2F5%29 So plug in the given slope to find the perpendicular slope



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


So the perpendicular slope is -5



So now we know the slope of the unknown line is -5 (its the negative reciprocal of 1%2F5 from the line y=%281%2F5%29%2Ax%2B6%2F5). Also since the unknown line goes through (0,-7), 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%2B7=-5%2A%28x-0%29 Plug in m=-5, x%5B1%5D=0, and y%5B1%5D=-7



y%2B7=-5%2Ax%2B%285%29%280%29 Distribute -5



y%2B7=-5%2Ax-0 Multiply



y=-5%2Ax-0-7Subtract -7 from both sides to isolate y

y=-5%2Ax-7 Combine like terms

So the equation of the line that is perpendicular to y=%281%2F5%29%2Ax%2B6%2F5 and goes through (0,-7) is y=-5%2Ax-7


So here are the graphs of the equations y=%281%2F5%29%2Ax%2B6%2F5 and y=-5%2Ax-7




graph of the given equation y=%281%2F5%29%2Ax%2B6%2F5 (red) and graph of the line y=-5%2Ax-7(green) that is perpendicular to the given graph and goes through (0,-7)