In Hartshonre p103, it is mentioned the two definitions of projective morphism coincide:
1)Let $f:X\to Y$ be a morphism, it is projective if it factors through a closed immersion followed with canonical map: $X\to \mathbb{P}^n_Y\to Y$, for some $n$.
2)Let $f:X\to Y$ be a morphism, it is projective if it factors through a closed immersion followed with canonical map: $X\to Proj(\mathcal{E})\to Y$, where $\mathcal{E}$ is a graded quasi-coherent algebra over $Y$.
When $Y$ is quasi-projective over a noetherian ring $A$, how to show the second implies the first one? Is there a reference for that?