SOLUTION: Hi! I need help in the following questions, it's only two. Please help and explain how and why you got what you got. Directions: Write an equation for the line that is perpendi

Algebra ->  Linear-equations -> SOLUTION: Hi! I need help in the following questions, it's only two. Please help and explain how and why you got what you got. Directions: Write an equation for the line that is perpendi      Log On


   

Question 534332: Hi! I need help in the following questions, it's only two. Please help and explain how and why you got what you got.
Directions: Write an equation for the line that is perpendicular to the given line and that passes through the given point.
1. (-1,-4); y= 1/6x+1
2. (-5,5); y= -5x+9
Please help, I know how to do it but when they twist it up like this i really don't get it. Please show all of the work and steps involved, and why. Thanks!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
(-1,-4)
+y+=+%281%2F6%29%2Ax+%2B+1+
This is in the form +y+=+m%2Ax+%2B+b+, where +m+ = slope
ANY line perpendicular to this line
will have slope = +-+1%2Fm+
Your equation has +m+=+1%2F6+, so any line
perpendicular to it has slope = +-+%281%2F%281%2F6%29%29+=+-6+
----------------
So far you have +y+=+-6x+%2B+b+. To find b, plug in
(x,y) = (-1,-4)
+-4+=+-6%2A%28-1%29+%2B+b+
+-4+=+6+%2B+b+
+b+=+-4+-+6+
+b+=+-10+
The equation of the perpendicular line is +y+=+-6x+-+10+
-----------------
(2)
(-5,5)
+y+=+-5x+%2B+9+
Slope of any perpendicular line = +-%281%2F%28-5%29%29+=+1%2F5+
Now plug in (x,y) = (-5,5)
+5+=+%281%2F5%29%2A%28-5%29+%2B+b+
+5+=+-1+%2B+b+
+b+=+6+
The equation is +y+=+%281%2F5%29%2Ax+%2B+6+
Here's a plot of these 2 lines:
+graph%28+400%2C+400%2C+-12%2C+12%2C+-12%2C+12%2C+-5x+%2B+9%2C+%281%2F5%29%2Ax+%2B+6%29+