R={(L1​,L2​):L1​ is parallel to L2​}R is reflexive as any line L1​ is parallel to itself i.e., (L1​,L1​)∈R.Now,Let (L1​,L2​)∈R.⇒L1​ is parallel to L2​⇒L2​ is parallel to L1​⇒(L2​,L1​)∈R∴R is symmetric.Now,Let (L1​,L2​),(L2​,L3​)∈R.⇒L1​ is parallel to L2​. Also, L2​ is parallel to L3​⇒L1​ is parallel to L3​∴R is transitive.Hence, R is an equivalence relation.The set of all lines related to the line y=2x+4 is the set of all lines that are parallel to the line y=2x+4Slope of line y=2x+4 is m=2It is known that parallel lines have the same slopes.The line parallel to the given line is of the form y=2x+c, where c∈R.Hence, the set of all lines related to the given line is given by y=2x+c, where c∈R.