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Only when you need

I posed this problem in class:

In a certain city, gas service is paying 15 € fixed a month and 0.75 € for each cubic meter consumed.

  1. How much do you pay for 3 m^3? And for 5 m^3
  2. Plot the function which relates consumed cubic meters and the cost of the service

When do you need the formula of the relation there? Clearly you could get (a) without a formula. And you could plot the points using value table (with previosly calculated values in (a) if you want) but you need the formula of the relation (cost = 15 + 0.75 meter) for assuring that you could join the points with a straight line (using the theoric fact that: afine functions correspond to straight lines). Otherwise you would not know if the plot is a straight line or a curve.

My students understood more clearly the connection between plots and functions when I ask them for which step needs here the formula.