May someone answer this hard math question for me?

Im thinking line x, because the coordinates on lines y & e and f & z are the same, but flipped (first touching point for f is (3, 1) and first touching point for e is (1, 3). It gives the rules for lines y & e and f & z, but not for x? And line x is the only one that doesn't have another line like this.

i can answer this if i have the answer choices