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Q: What is the minimum number of points needed to identify a line?

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how do you identify points of contention

2 points

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depends on the position of the points if points are collinear, we have just only one line, the minimum number. If points are in different position (if any of the two points are not collinear) we have 21 lines (7C2), the maximum number of lines.

Yes, ordered pairs identify points in a coordinate plane. If that doesn't answer your question, please restate it (say it another way).

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3

The minimum is two points, one point at each end of the line.

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A minimum of 6 sets of data are needed to make a valid conclusion.

There can be no minimum number - it is simply not possible. Given any n points in 3-dimensional space, it is possible to find a polynomial that will generate a curve going through each of those points. There are other functions which will also do the trick. So, given any number of points, it would be impossible to determine whether they were generated by a fractal or a polynomial (or other function).

There is no minimum number - it is simply not possible. Given any n points in 2-dimensional space, it is possible to find a polynomial of order (n-1) that will generate a curve going through each of those points. There are other functions which will also do the trick. So, given any number of points, it would be impossible to determine whether they were generated by a fractal or a polynomial (or other function).

min 3, but more would be better. The max/min point is a must and a couple of points to the left and right of it.

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In Euclidean geometry each line contains a minimum of an infinite number of points. In projective geometry, though, a line may have as few as two points.

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how do you identify points of contention

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