How to show plane is an affine plane?

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I know what an affine plane is .But I don't know how to prove that a plane is an affine plane. Can give me a proof example?

For example, prove that (P,L)is an affine plane:

P is the set of ordered pairs of numbers (x,y)(p.s (x,y)is not equal to (y,x))

L is p(x,y) that satisfying ax+by=c