Two cones over a projective variety

Question

Let $A$ be a commutative graded algebra over a field $k$ and $X=\operatorname{Proj}(A)$ is a smooth scheme, then $E=\oplus_{i \geq 0} \mathcal O_X(i)$ is a quasi-coherent sheaf of algebras on $X$. I can take relative $\operatorname{Spec}E$, geometrically this is total space of the line bundle $\mathcal O_X(-1)$. How $\operatorname{Spec}E$ is related to $\operatorname{Spec} A$? Where $\operatorname{Spec} A$ is just spectrum of the ring $A$ as commutative ring, that is geometrically a cone over $X$ in affine space .