Short answer: do as the question says. There is no ambiguity.
Long answer:
This has little to do with independent and dependent variables. This is a coordinate transformation, which transforms a curve into a linear line so a line of best fit can be drawn (because no one is capable of drawing a hyperbola of best fit). The resulting linear line has two easily determinable parameters: the gradient and y-intercept. A formula would then be provided to interpret these quantities. Such interpretation only works when x and y are as specified by the transformation.
In this case, the transformation requires t and 1/t to be on the x axis. Regardless of which is the independent variable, the interpretation dictates that the graph must be set up this way.
(Of course, you can transpose the linear fit to take the inverse, etc etc.)