mortgage of home equity line of credit

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I own my residence.
How does a home equity line of credit work?
Can I get one to buy a house that I would plan to live in, using my present residence as a rental, or possibly selling it?
Apparently they are a bit more expensive than a mortgage on my residence.
Could I get a mortgage on my residence to buy a house I planned to move into, using this one as a rental?
Is it more advantageous to get a mortgage rather than a HELOC?
ofgift