What do we call a metamorphic rock that has microscopic to very fine-grained texture, breaks into slabs or sheets and is dull on the surface?

Slate.

Explanation:

Slate is a fine-grained homogeneous metamorphic rock derived from an original shal sedimentary rock composed of clay or volcanic ash through regional metamorphism. It is the finest grained foliated metamorphic rock

Slate is formed by shale and mudstone in the basin are compressed by horizontal forces with little heating. These forces and heat modify the minerals in the shale and mudstone. Foliation may not correspond to the original sedimentary layering, but instead is in planes perpendicular to the direction of metamorphic compression.

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