Graphing Intercepts

Date: 11/06/97 at 22:16:05
From: Scott J. Guenther
Subject: Help on Algebra graph intercepts

Hi.  

How would I find the intercept for a problem such as 3x-2y = 12?

Any help would be appreciated.  Thanks.

Date: 11/10/97 at 11:18:44
From: Doctor Otavia
Subject: Re: Help on Algebra graph intercepts

Hello!  

When you speak of intercepts, it helps to know which one you're 
referring to. In the plane, unless a line is parallel to either the 
x-axis or the y-axis, it will intersect both axes sometime. We know 
this because two non-parallel lines in the same plane will intersect 
sometime.

So then, since I'm not sure which intercept you want, I'll show you 
how to find both the x-intercept, or where the line intersects the 
x-axis, and the y-intercept, where the line interesects the y-axis.  

One really easy way to think about this is to try to visualize the 
problem. Where will a line intersect the x-axis? If you draw it, 
you'll see that it will always interesect the x-axis at a point 
where the y-coordinate is 0. This applies also to the y-intercept, 
but in reverse - a line will intersect the y-axis at a point where 
the x-coordinate is 0. So one way to solve this problem is to set 
x = 0 and solve for y, thus finding the y-intercept, and then set 
y = 0, solve for x, and find the x-intercept.  

Another way to do this is to put your line into slope-intercept form.  
That is when the equation for the line is in the form 
  
   y = mx + b

where m is the slope and b is the y-intercept.

(Really, this is the same as the other way, because when x = 0, 
y = b.)

Then the x- intercept is

   -b
  -----
    m

(which is the same as setting y = 0.)  So you see, either way works.  

I hope this helps!

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