



OK,
maybe we don't have an equation 


we
just have two points. 


And
we want to know what equation line 


goes
through both of them. 





Maybe
we have the points X = 1, Y = 2 (1,2) 


and
the point X = 5, Y = 3 (5,3). 











We
want to figure out what equation 


has
a graph line that goes through these two points. 





How
do we do it? 





Well
we know that when we DO figure out 


what
the equation is, 


these
two points will be part of it. 





We
can use these two points to figure out 


what
the slope of the line is. 





Remember
... 








So: 








The
slope is ^{1}/4. 


That
means when we do find the equation 


that
goes through the two points, 


it will
look like this ...












But
what is the something? 





Here's
how we find out ... 





Choose
either one of the points 


as
the values X_{1} and Y_{1} 


and
use the formula ... 








Let's
chose the point where X = 1 and Y = 2 ... 











Multiply
out the right side ... 











Add
2 to each side to get 


Y
by itself on the left side ... 











The
equation line that goes through 


both
of our points is ... 











Let's
look at that formula again. 





When
we have any point and the slope of the line 


the
equation for the line can be found using ... 





Y  Y_{1}
= m(X  X_{1}) 





and
we can find the m (the slope) 


if
we know any two points on the line ... 











If
we really want something that looks impressive, 


we
can put the formula for finding the slope 


into
the formula for finding the line. 


We
would get ... 











That
last equation is called: 





The Two
Point Equation of a Line






Ya
know, I'm glad we're done with that. 


That
was a ton of stuff about two points. 


I
bet there's not one more thing 


we
could do with two points! 





Then
again ... 





copyright 2005 Bruce Kirkpatrick 
