Let $X=\mathrm{Spec}(R)$ be an affine scheme and $Z=\mathrm{Spec}(R/I)$ be a closed subscheme of $X$ defined by an ideal $I$ of $R$. The blow up of $X$ along $Z$ is (say)$\mathrm{Bl}_{Z}(X)=\mathrm{Proj}(\bar{R})$, where $\bar{R}$ is the Rees algebra of $I$ over $R$, i.e., $\bar{R}=R \oplus I +\oplus I^2 \oplus I^3 \oplus \cdots $.
The blow-map $\mathrm{Bl}_Z(X)\rightarrow X$ is given by the natural ring homomorphism $R\rightarrow \bar{R}$.
My question is: How does the natural ring inclusion $R\rightarrow \bar{R}$ to give rise to a map $\mathrm{Proj}(\bar{R})\rightarrow \mathrm{Spec}(R)$?