In which scenario can you reverse a dependent and independent variable and still have a meaningful world interpretation of slope

Answer: A independent variable is one that you can change, and cause a response in a dependent variable.

For example, the time that some food is in the microwave will affect the temperature of it, and you can set the time, but in this case you can't "reverse", because you cant set the temperature.

But suppose you have a experimental microwave, in which you can set a time and the temperature will depend on the time, or you can set the desired temperature of the dish inside and the microwave sets the time in function of that, in this case the variables are reversible.

Other example, if you have a cellular phone, you can play with it for some time and see how is the change in the battery (where time is the independent and battery the dependent). Or play with ir until the battery is half charged and then measure the time you played (the charge of the battery is the independent and the time is the dependent) And the slope goes from "how much battery consumes in function of time" to "How much time is needed to consume a percentage of battery"

For the answer to the question above, As the amount of fuel consumed by a vehicle increases, the distance traveled by the vehicle increases. Reversed: As the distance traveled by the vehicle increase, the amount of fuel consumed by a vehicle increases