eli5: why 3 pairs (or maybe 2?) of cleartext and ciphertext letters are needed to determine an affine cipher?

Question

eli5: why 3 pairs (or maybe 2?) of cleartext and ciphertext letters are needed to determine an affine cipher?

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Answer 1

Essentially it comes down to an affine cipher being a line.

It maps letters to numbers, then remaps them using a linear function (like mx + b). The issue is with a line is if you know two points along a line you can calculate the whole line, so two pairs of letters is enough to solve for the line which solves for the cipher.