Equation of a Line in Point-Slope, Slope-Intercept, General Form

Date: 8/2/96 at 1:58:36
From: Alfred T Chu
Subject: Finding the Equation of a Line

Hello Dr. Math,

How do I find an equation of the line L that contains the point 
(4, -4) and is perpendicular to the line that has the equation 
2x-5y+3 = 0?  I need the equation in:

  a. Point-slope form 
  b. Slope-intercept form
  c. General form

I am practicing problems from a math workbook and having problems 
doing it.  Thank you very much for helping me!

Sincerely,

Alfred

Date: 8/2/96 at 13:21:33
From: Doctor Anthony
Subject: Re: Finding the Equation of a Line

The slope of the line 2x-5y+3 = 0 is found by putting this in the 
y = mc+c from 5y = 2x+3   so  y = (2/5)x + (3/5)  so slope is  2/5

A line perpendicular to this will have slope -5/2

The required line therefore has the equation 

    y+4 = -(5/2)(x-4)  This is the point slope form

   2y + 8 = -5x + 20 
       2y = -5x + 12
        y = -(5/2)x + 6   This is the slope intercept form

   5x + 2y - 12 = 0    This is the general form

-Doctor Anthony,  The Math Forum
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