Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

solution:

Once more, The arrangement of all lines identified with the line y = 2x + 4, is the arrangement of all its equal lines. Incline of given line is m = 2.

As we probably are aware slant of all equal lines are same.

Subsequently, the arrangement of all identified with y = 2x + 4 is y = 2x + k, where k ∈ R.