Correct. It was given at Horeb in memory of the persecution suffered as slaves. A day of rest for those who had none in their former lives as slaves:
“I am the Lord your God, who brought you out of Egypt, out of the land of slavery…”
“Observe the Sabbath day by keeping it holy, as the Lord your God has commanded you. Six days you shall labor and do all your work, but the seventh day is a sabbath to the Lord your God. On it you shall not do any work,… Remember that you were slaves in Egypt and that the Lord your God brought you out of there with a mighty hand and an outstretched arm. Therefore the Lord your God has commanded you to observe the Sabbath day." - Deut 5
Similarly, Exodus 20:
“I am the Lord your God, who brought you out of Egypt, out of the land of slavery."…
“You shall have no other gods…”
“You shall not make for yourself an image…”
“You shall not misuse the name of the Lord your God…"
“Remember the Sabbath day by keeping it holy. Six days you shall labor and do all your work, but the seventh day is a sabbath to the Lord your God. On it you shall not do any work, neither you, nor your son or daughter, nor your male or female servant, nor your animals, nor any foreigner residing in your towns." [end of original]
Verse 11 was added to Exodus 20 some time after it was written, after the (later) work of Genesis was completed - in order to tie the two together:
For in six days the Lord made the heavens and the earth, the sea, and all that is in them, but he rested on the seventh day. Therefore the Lord blessed the Sabbath day and made it holy.
The Sabbath is a gift given at Horeb directly to the ex-slaves specifically because they were slaves. A day of rest from hard labor for those who previously had none. No other reason was originally given.