Algebra 1 Two Point Equation of a Line
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Connect The Dots
Two Point Equation of a Line

 
 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 X1 and Y1
 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 - Y1 = m(X - X1)

 
 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

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