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Question 1032649: Find the equation for the line that passes through the point (1, 5), and that is perpendicular to the line with the equation 9x - 3y = -18.
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39617)   (Show Source):
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
That's no explanation at all! It's just a magic trick
method that works.
9x - 3y = -18
{His magic trick: Swap the letters on the
left
9y - 3x
change one of the signs,
9y + 3x
substitute in
the point (1,5)
9(5) + 3(1) = 45 + 3 = 48
set 9y + 3x equal to 48
9y + 3x = 48
Divided through by 3
3y + x = 16
and abracadabra, you have the answer!
But that's math-a-magic!, not mathematics.
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We are given a point (1,5) and the equation of a line that we
can easily graph by finding its intercepts (-2,0) and (0,6).
like this:
and we want a line that goes through the given point
that is perpendicular to the given line. In other words,
we want this red line:
The given line has equation
We get it in slope-intercept form by solving
for y:
Divide through by -3
Compare that to
So the given line's slope is m=3.
m=3/1 has a rise of 3 and a run of 1. The slope is
positive so it slopes uphill to the right.
A line perpendicular to it will have the rise and
run swapped but it will slope downhill to the right.
So its slope will have the run and rise swapped as
1/3 and will be negative because it slants downhill
to the right. So its slope is -1/3.
Then we use the point-slope formula:
Point-slope formula:
y - y1 = m(x - x1)
where m=-1/3 and (x1,y1) = (1,5)
  
 
Multiply through by LCD = 3
 
Add x to both sides and then 15 to both sides:
Same as with the magic trick.
Edwin
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