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.
- How much do you pay for \(3 m^3\)? And for \(5 m^3\)
- 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.