Final answer:
The sun's apparent east-to-west movement across the sky is due to Earth's rotation from west to east, which causes celestial objects to appear to move in the opposite direction.
Step-by-step explanation:
The sun appears to move from east to west across the sky each day because Earth rotates from west to east. This eastward rotation of Earth causes celestial objects, including the sun, to appear to move in the opposite direction across the sky. The idea of celestial bodies moving in paths -- such as the ecliptic for the sun -- is part of the reason for this apparent motion. Moreover, Earth must complete a little more than one rotation relative to the stars for the sun to appear at the same point in the sky on the next day, explaining the solar day.