The really short answer is, there are 5 weeks, and the temperature dropped a total of -15 celsius on those 5 weeks, how many times does 5 go into -15? -15/5 or -3, so each week, evenly it dropped -3 celsius, and after 5 weeks, it added up to -15 celsius total from the first one.
so in the first week, or week 1, it dropped -3(1), on week 2 it dropped -3(2) on week "w" it dropped -3(w), f(w) = -3w.