Universal quotient line bundle (${\pi }^{\ast }E\twoheadrightarrow {\mathcal{O}}_{\mathbb{P}(E)}(1)$)

On the projectivization by quotients, the fibre over a one-dimensional quotient of $E_x$ is that quotient line itself. These lines glue to the universal quotient. Its restriction to a projective fibre has degree one. It is the dual of the relative tautological line after identifying quotient projectivization of $E$ with line projectivization of $E^{\ast }$.