Associated Topics || Dr. Math Home || Search Dr. Math

### 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/
```
Associated Topics:
High School Basic Algebra
High School Equations, Graphs, Translations
Middle School Algebra
Middle School Graphing Equations

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search