Hill was born in Dallas, Texas. He and his brother Rocky Hill (also a musician) were raised in the Lakewood neighborhood of East Dallas. He attended Woodrow Wilson High School (Dallas) where he played the cello.\n', '

Hill, his brother the guitarist Rocky Hill and future fellow ZZ Top member Frank Beard played in local Dallas bands the Warlocks, the Cellar Dwellers, and American Blues. From 1966 to 1968, American Blues played the Dallas-Fort Worth-Houston circuit. In 1969, Hill was a member of a fake version of the British band The Zombies with Beard.\n', '

In 1968, the band decided to leave the Dallas–Fort Worth area and relocate to Houston. At this time, however, Rocky Hill wanted to focus on "straight blues", while Dusty wanted the band to rock more. Rocky left the band and Dusty and Beard moved to Houston, joining guitarist/vocalist Billy Gibbons of Houston psychedelic-rockers Moving Sidewalks in the recently formed ZZ Top just after they released their first single in 1969.\n', '

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