Assuming that each (square) pixel has the same angular scale (not a given if the field of view is large) of $theta$ degrees/pixel.
Then the declination (in degrees): $delta simeq delta_0 + theta y$
The right ascension (in degrees): $alpha simeq alpha_0 - theta x/cos delta$
where $alpha_0$ and $delta_0$ are the RA and Dec at $x=0$, $y=0$. [The minus sign is there because right ascension increases towards the left of a sky image.]
This approximatimation becomes poor as the field of view gets larger.
A slightly more complex, but accurate, approach is described in http://gtn.sonoma.edu/data_reduction/astrometry.php
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