How do credit card machines read that little black line?

It’s a magnetic strip. It’s read just like a VCR reads a video tape.

Or the same way a tape player reads a cassette tape.

To put it simply, a small band of Pygmie tribesman are glued to that black strip. When you swipe the card the tribesman are trained to raise their hands in a certain pattern which corresponds to your account. Simple.

By the way, the tribesman subsist on the lint in your wallet

So no one actually knows this answer. And can not give me a detailed explanation.

“The stripe on the back of a credit card is a magnetic stripe, often called a magstripe. The magstripe is made up of tiny iron-based magnetic particles in a plastic-like film. Each particle is really a tiny bar magnet about 20-millionths of an inch long.
The magstripe can be “written” because the tiny bar magnets can be magnetized in either a north or south pole direction. ”
http://money.howstuffworks.com/personal-finance/debt-management/credit-card2.htm