Section 1.1 & 1.2: Types of Relations

Let \(L\) be the set of all lines in \(XY\) plane and \(R\) be the relation in \(L\) defined as
\[R = \{(L_1, L_2) : L_1 \text{ is parallel to } L_2\}\]
Show that \(R\) is an equivalence relation. Find the set of all lines related to the line \(y = 2x + 4\).