Expert: Chanda Walker - 1/27/2009

Question
I am having a difficult time understanding how to do this. I don't understand how to write the equation of a line that is perpendicular to a given line and point.
The equation I am having trouble with at this moment is
-2X+Y=-3 (2,-5)

Answer
Ok here are the steps.

1)  find the slope of the given line
2)  find the slope of the perpendicular line, which is given by -1/m where m is the slope of the given line
3)  substitute the point you have been given in the equation:

y = m x + b

where m is the perpendicular slope so that you can solve for b.
4)  Viola!  You're finished.  Just put the perpendicular slope in for m and the b you found into the following equation

y = m x + b

I'll help you with this problem.

1)  the slope of the given line
-2x + y = -3
y = 2x - 3

SO m must equal 2.

2)  the slope of the perpendicular line is -1/2

3)  substitution
-5 = -1/2 (2) + b
-5 = -1 + b
b = -4

4)  Your new line is:
y = (-1/2) x - 4

Make sense?  Let me know if you need further help.