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### Intercept of Two Lines

```
Date: 06/07/99 at 13:45:20
From: Jeff Burger
Subject: Locate intercept of two sloping lines

Helping my son with math has started to stretch my abilities a little.
I also found that I could use this in my work if I could solve it.

We need to locate the intercept point of two lines. If the y = mx + b
is given (standard form) for two lines, how do we calculate the exact
location without graphing.

Basically then

y = m1*x + b1 = m2*x + b2

or
m1*x + b1 = m2*x + b2

then
m1*x = m2*x + b2 - b1

then
x = m2*x + b2 - b1
--------------
m1

How do I isolate "x"?
```

```
Date: 06/07/99 at 17:52:36
From: Doctor Arthur
Subject: Re: Locate intercept of two sloping lines

Jeff,

It looks as if you started off really well, but you forgot to combine
like terms. You were correct when you said m1*x = m2*x + b2 - b1, but
instead of dividing by m1, subtract m2*x from both sides to get:

m1*x - m2*x = b2-b1

If you factor x, you get

x(m1-m2) = b2-b1

Then just divide both sides by (m1-m2) and you get

x = (b2-b1)/(m1-m2)

Remember that b1, b2, m1, and m2 are all real numbers; therefore your
answer is either some type of fraction, or an integer.

I hope that this answers your question, and that you'll come back with
other questions you may have.

- Doctor Arthur, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
High School Equations, Graphs, Translations

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