Equations for Lines

Date: 5/29/96 at 16:19:0
From: CHAD E MILBURN
Subject: Algebra Wordproblem

Dear Dr. Math, 

My brother is taking a correspondence course in Algebra 2 and there 
are a couple of word problems we can't figure out. I have tried 
helping him but word problems I cannot do!

1. Write an equation, in standard form, of the line containing the 
point P(1,-3) that is parallel to the line whose equation is 2x-y=3.

2.  Write an equation, in standard form, of the line containing  
Q(-5,4) that is perpendicular to the line whose equation is 3x-2y=8.

Date: 5/30/96 at 14:19:6
From: Doctor Darren
Subject: Re: Algebra Wordproblem

1. We know that this line can also be written in the form y=2x-3, so 
it and all lines parallel to it have slope = 2.  We now have a point 
on our line and its slope, so we can write the line in point-slope 
form as:  

     (y-(-3)) = 2(x-1)
          y+3 = 2x-2
         2x-y = 5


2. The line 3x-2y=8 has slope equal to 3/2.  We know that if two lines 
are perpendicular then their slopes are negative reciprocals of each 
other (i.e. if a line has slope m, all lines perpendicular to it have 
slope -1/m). So the slope of the line that we want is -2/3. As in the 
previous problem, we now have the slope of the line and a point on the 
line.  Therefore, the line can be written in point-slope form as:

    y-4 = (-2/3)(x-(-5))
    y-4 = (-2/3)x - 10/3
  3y-12 = -2x-10
  3y+2x = 2

I hope this helps!

-Doctor Darren,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/