How many lines are determined by $n$ coplanar points (no three of which are collinear)?

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I have a problem in which I need to find how many lines there would be if there are n points. No 3 points are collinear. All points are coplanar. I have figured out this much:

Lines	Points
0	1
1	2
3	3
6	4
10	5
15	6
So on...

I have noticed that the increment between the number of lines is one.
So:
0 + 1 = 1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
Thank you!

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1 Answer

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@JonathanMiller has a website that has the answer. The formula is: $$ \frac{x(x-1)}{2} $$

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