SOLUTION: Write an equation for a line perpendicular to 4y−16x=16 and passing through the point (12,2)

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Question 1019376: Write an equation for a line perpendicular to 4y−16x=16
and passing through the point (12,2)
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
4y=16x+16
y=4x+4, dividing by 4.
the slope is 4
The slope of the perpendicular line is the negative reciprocal or -1/4
point slope formula
y-y1=-(1/4)(x-x1)
y-2=(-1/4)(x-12)
y-2=(-x/4)+3
y=(-x/4)+5
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C4x%2B4%2C%28-x%2F4%29%2B5%29

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

4y-16x=16.............both sides divide by 4
4y%2F4=16x%2F4%2B16%2F4
y=4x%2B4
and if passing through the point (12,2), we have:
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 4, 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%284%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F4%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%2F4 Multiply the fractions.


So the perpendicular slope is -1%2F4



So now we know the slope of the unknown line is -1%2F4 (its the negative reciprocal of 4 from the line y=4%2Ax%2B4). Also since the unknown line goes through (12,2), 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=%28-1%2F4%29%2A%28x-12%29 Plug in m=-1%2F4, x%5B1%5D=12, and y%5B1%5D=2



y-2=%28-1%2F4%29%2Ax%2B%281%2F4%29%2812%29 Distribute -1%2F4



y-2=%28-1%2F4%29%2Ax%2B12%2F4 Multiply



y=%28-1%2F4%29%2Ax%2B12%2F4%2B2Add 2 to both sides to isolate y

y=%28-1%2F4%29%2Ax%2B12%2F4%2B8%2F4 Make into equivalent fractions with equal denominators



y=%28-1%2F4%29%2Ax%2B20%2F4 Combine the fractions



y=%28-1%2F4%29%2Ax%2B5 Reduce any fractions

So the equation of the line that is perpendicular to y=4%2Ax%2B4 and goes through (12,2) is y=%28-1%2F4%29%2Ax%2B5


So here are the graphs of the equations y=4%2Ax%2B4 and y=%28-1%2F4%29%2Ax%2B5




graph of the given equation y=4%2Ax%2B4 (red) and graph of the line y=%28-1%2F4%29%2Ax%2B5(green) that is perpendicular to the given graph and goes through (12,2)