SOLUTION: How do you write an equation in the variables x and y for the line that passes through the point (18,14) and that is perpendicular to the line 9x+6y=174.

Algebra ->  Equations -> SOLUTION: How do you write an equation in the variables x and y for the line that passes through the point (18,14) and that is perpendicular to the line 9x+6y=174.      Log On


   

Question 1091255: How do you write an equation in the variables x and y for the
line that passes through the point (18,14) and that is
perpendicular to the line 9x+6y=174.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

First we find the slope of the line 9x+6y=174
by solving it for y to get it in slope-y-intercept form,
which is y=m%2Ax%2Bb:

9x%2B6y=174
6y=-9x%2B174

expr%286%2F6%29y=expr%28%28-9%29%2F6%29x%2B174%2F6

y=expr%28-3%2F2%29x%2B29

We compare that to the slope-y-intercept form 

y=m%2Ax%2Bb

we see that the slope is -3%2F2

Then we remember that perpendicular lines have slopes 
which are opposite signed reciprocals of each other.

Therefore the slope of a line perpendicular to a line
with slope -3%2F2 has slope %22%22+%2B+2%2F3.

Now we use the point-slope formula

y-y%5B1%5D=m%28x-x%5B1%5D%29 with (x1, y1) = (18,14),
and m=2%2F3

y-14=expr%282%2F3%29%28x-18%29

Multiply both sides by 3 to clear the fraction:

3y-42=2%28x-18%29

3y-42=2x-36

-2x%2B3y=6

We want it to begin with a positive term in x, so that
it will be in the same form as the given equation, so we
we multiply through by -1 

2x-3y=-6



The Green line is the graph of the Given line 9x+6y=174.
The Red line is the graph of the Required line 2x-3y=-6.

Edwin