# ANOVA representation

This question can seem quite stupid.

I know that there are two ways of representing ANOVA model. For example, in one-way ANOVA the model can be written as: $$y_{ij} = \mu + a_j + e_{ij}$$ where $i$ indicates subject, $j$ indicates some factor

Also it can be written as: $$y_i = ax_i+b + e_i$$ where $a$ and $b$ are some parameters and $x$ is indicator variable that takes $0$ or $1$.

My question is why the first representation is used mostly in literature? I understand that my opinion is only subjective but representation as a linear model for me seems more understandable in the sense of I know how to fit it and how to get the parameters.