The Projective Space - Definition 1:
The underlying set is the set $P^{n}(\Bbb{R})$ of lines in $\Bbb{R}^{n+1}$ passing through the origin. There is another way of looking at $P^{n}(\Bbb{R})$.
On $\Bbb{R}^{n+1} - {0}$ we introduce the equivalence relation", defined as follows: $x R y <=> \lambda x = y$ with $\lambda \in \Bbb{R},\lambda \neq 0$
Definition 2:
An equivalence class $[x]$ containing $x \in \Bbb{R}^{n+1}$ can be identified with the line through the origin in $\Bbb{R}^{n+1}$ joining any point in the equivalence class.
I am trying to understand how definiton 2 is equivalent to definition1 or how can I understand definition 2 from definition 1?