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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?

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    Welcome to math.stackexchange. Your answer sounds good. What do you mean by general? You could parameterize the line as follows, let $(x_1,y_1) = \vec{d}$ and $(x_2,y_2) = \vec{w}$ then $\vec{x} = (x,y) = (x_1 \cdot t + x_2, y_1\cdot t + y_2)$ – 2017-01-08

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Geometrically, for vectors $\overrightarrow{d}$ and $\overrightarrow{w}$, exery $\overrightarrow{x}$ obtains from a multiplier of $\overrightarrow{d}$ which adds to $\overrightarrow{w}$:

enter image description here

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 $C$)