Given 100 noncollinear points, make a conjecture about the maximum number of lines formed.

The number of distinct points required to determine a
unique line are 2. In the question asked there are 100 non-collinear points. Each of
them can determine 99 unique lines with the other
points.

But it has to be kept in mind that a line
determined by two points A and B is the same even if the position of the points is
interchanged, i.e. AB and BA are the same line.

This gives
the maximum number of lines that the points can determine as 100*99/2 =
4950

The maximum number of lines that 100
non-collinear points can determine is 4950.