What does $\overrightarrow{x} = t\cdot \overrightarrow{d} + \overrightarrow{w}, \space t \in \mathbb{R}$ and vectors are in $\mathbb{R}^2$, show geometrically?
My answer: Does $\overrightarrow{x}$ geometrically mean that it shows a line parallel to $\overrightarrow{d}$ and going through $\overrightarrow{w}$?
How can I describe a vector equation in general?
Geometrically, for vectors $\overrightarrow{d}$ and $\overrightarrow{w}$, exery $\overrightarrow{x}$ obtains from a multiplier of $\overrightarrow{d}$ which adds to $\overrightarrow{w}$:
as picture shows, and you said, $\overrightarrow{x}$ geometrically shows a line parallel to $\overrightarrow{d}$ and going through $\overrightarrow{w}$ (that line passed through point $C$)