The sentence above is an example of the rule it describes!
“As a general rule” is incomplete; it can’t stand on its own. That makes it a dependent clause.
“Use a comma when a dependent clause precedes an independent clause” is complete; it can stand on its own. That makes it an independent clause.
The comma in the first sentence of this post is doing a legitimate job. It separates the dependent clause from the independent clause that follows it.
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