Equivalence Classes Relationships

Question in attachment is as follows:
Consider all lines in the plane. If a relationship between 2 lines is defined by the expression that their slopes are equal, prove that this relationship is an equivalence relationship.

If we consider the set of all lines in the plane, how would you uniquely identify the equivalence classes?

(Formulas and remainder of question found in attachment)

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... is true (trivial - a line has the same slope as itself)
sym : x R y => y R x is true (since x has the same slope as y, y obviously has the same slope as x)
trans : x R y ...