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

### Equations in Intercept Form

```
Date: 08/27/98 at 17:58:47
From: cole
Subject: Intercept form

Show that an equation for a line with nonzero x-intercepts and
y-intercepts can be written as:

x/a + y/b = 1

where a is the x-intercept and b is the y-intercept. This is called the
intercept form of the equation of a line.

I do not understand what they want me to do. Do I solve it like this:
bx + ay - ab = 0? Or do I substitute with variables? Can you
```

```
Date: 08/27/98 at 18:59:01
From: Doctor Jaffee
Subject: Re: Intercept form

Hi Cole,

There are a number of ways to approach this problem. I'll present two

First of all, let's consider the situation geometrically. What is an
x-intercept? If you say that it is a point on the x-axis where the line
crosses, you are right. But what is the y value at that point? If you
say 0, you are right again. So, let's go back to the equation
x/a + y/b = 1 and replace the y with a zero. You get x/a = 1, which
means x must equal a. Now putting this back into geometric terms, we
have "when the line crosses the x-axis (that is, when y = 0), the x
number must be a (that is, the x-intercept is a).

Likewise, the y-intercept is the point where the line crosses the
y-axis, and at that point x must equal 0. If you substitute 0 for x in
the original equation you eventually end up with y = b, or in other
words, the y-intercept is b.

Let's look at a second approach. Suppose we start with the equation
Ax + By = C. It is important to note that "A" doesn't mean the same as
"a". Capital letters generally mean some different value from lower
case letters.

If we divide both sides by C, we get (A/C)x + (B/C)y = 1. Suppose we
are told that a and b are the x- and y-intercepts, respectively. That
means that (a,0) and (0,b) are points on the line. If we substitute
a for x and 0 for y we get (A/C)*a = 1. That means that A/C must equal
1/a.

Furthermore, if we substitute 0 for x and b for y, we get B/C = 1/b.

Therefore x/a + y/b = 1 is the equation.

I hope this explanation has helped. Write back if it needs further
clarification and I or one of the other Doctors will try to help you
out. Also, write back with any other questions you have.

- Doctor Jaffee, The Math Forum
Check out our web site! http://mathforum.org/dr.math/
```
Associated Topics:
High School Linear 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