SOLUTION: I found the 2 point equation and cannot find one for 3 point. I need help writing a 3 point equation of the line. (0,4) (2,6) (3,7) y=__x plus ____

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Question 587490: I found the 2 point equation and cannot find one for 3 point.
I need help writing a 3 point equation of the line.
(0,4)
(2,6)
(3,7)
y=__x plus ____

Found 2 solutions by richwmiller, solver91311:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!

Find the line for (0,4) and (3,7)
See if (2,6) fits in the equation

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


You first have to check to see that the three points are collinear. If they are, then you can choose any two of the points and use the two-point form to write an equation of a line where the solution set contains all three points. On the other hand, if they are not collinear, you have to find the equation of a conic section that fits the data.

The three points are collinear if and only if the slopes of the lines containing any pair of the three points are equal. So first use the slope formula on any pair of the given points:



where and are the coordinates of the given points.

Then do it again for a different pair of the points. If the slopes are equal, then the points are collinear and you can use the two-point equation on any pair.

If they are not collinear, write back and we'll deal with the problem from there.

John

My calculator said it, I believe it, that settles it
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