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The voltage at the tap of a voltage divider (or Pot, as you have learned) depends on two things: the ratio of the resistor values above and below the tap, and, the current being drawn out of the tap....
Basically a makeshift voltage regulator. Or does that not really work?
In the case of the opamp circuit you posted, the current into the non-inv input of the 741 (input bias current) is very small (uA), so the voltage at the tap (wiper) is proportional to the wiper position from the bottom. However, if you tried to draw more than a few hundred uA from the tap, then the voltage would sag, like a poorly regulated power supply.
The math is fairly simple. The principle is "Thevenin's Equivalent". Google it.