This is the 2758th most frequent Japanese word.
表し
"Expression" or "representation."
In this sentence, '表していた' (arashiteita) conveys the act of expressing or representing emotions, specifically conveyed through his smile.
彼の笑顔は心からの喜びを表していた。
His smile expressed genuine joy.
Here, '表している' (arashiteiru) indicates representation or visualization, applied to how the graph shows data changes.
グラフはデータの変化を表している。
The graph represents the changes in the data.
In this context, '表していた' (arashiteita) reflects communication or expression, particularly demonstrating gratitude through her words.