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

.............both sides divide by


and if passing through the point (,), 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 , you can find the perpendicular slope by this formula:

where is the perpendicular slope


So plug in the given slope to find the perpendicular slope



When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second



Multiply the fractions.


So the perpendicular slope is



So now we know the slope of the unknown line is (its the negative reciprocal of from the line ). 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:

where m is the slope and (,) is the given point



Plug in , , and



Distribute



Multiply



Add to both sides to isolate y

Make into equivalent fractions with equal denominators



Combine the fractions



Reduce any fractions

So the equation of the line that is perpendicular to and goes through (,) is


So here are the graphs of the equations and




graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)
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