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/