SOLUTION: Find the equations for two lines that both go through the point (1,2), one with slope 3 and one with slope -1/3.

Algebra ->  Linear-equations -> SOLUTION: Find the equations for two lines that both go through the point (1,2), one with slope 3 and one with slope -1/3.      Log On


   

Question 1106045: Find the equations for two lines that both go through the point (1,2), one with slope 3 and one with slope -1/3.
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Just use the point slope formula:

y - y1 = m(x - x1)
where (x1,y1) = (1,2)

(a) using m = 3:

y-2=3%28x-1%29
y-2=3x-3
y=3x-1

That's this red line:



(a) using m = 1%2F3%29%29%29%3A%0D%0A%0D%0A%7B%7B%7By-2=expr%281%2F3%29%28x-1%29
Multiply both sides by 3
3y-6=x-1
3y=x%2B5
y=expr%28-1%2F3%29x%2B5%2F3

That's this green line:



They're perpendicular because their slopes are negative reciprocals,
which is the same as saying that when you multiply their slopes
together, you get -1.  %283%5E%22%22%5E%22%22%29%28-1%2F3%29=-1
 
Edwin