Parallel Lines

Date: 9/3/96 at 13:10:58
From: Anonymous
Subject: Parallel Lines

Could you please help us students (Emma and Marie), as we are not 
getting anywhere on this question in our textbook.

  "The lines y=kx+4 and 3y=(k+3)x-5 are parallel. Find k."

Can you explain how to do it, please? Many thanks.

Emma and Marie.

Date: 9/3/96 at 14:2:48
From: Doctor Mike
Subject: Re: graphs.
  
You first need to get both line equations is slope-intercept form.  
The first one is in that form already. To get the second one in that 
form you divide both sides by 3, giving
   
         k+3      5   
   y  =  --- *x - ---
          3       3 
  
For the lines to be parallel the slopes have to be the same, so k must 
equal (k+3)/3 , and that is easily solved as k=3/2 .  The two lines 
are y=(3/2)x + 4 and y=(3/2)x - (5/3).  Each has the slope 3/2 and 
they intersect the y-axis at (0,4) and (0,-(5/3)) .
  
I hope this helps.  Write back if you have other questions.   

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