Writing the Rule

Many prices are a function. A music school charges a 25 dollar sign-up fee plus 10 dollars per lesson. The cost depends on one thing, the number of lessons n, so the cost is a function of n: C(n) = 25 + 10n.

Build the rule from the two kinds of charge. The fee is paid once, however many lessons you take, so it is a number on its own. The 10 dollars is paid for every lesson, so it multiplies n. A fixed part plus a rate times the input is the shape of every rule like this.

The rate is the average rate of change from the last chapter: each extra lesson adds 10 dollars, so the cost rises 10 for every 1 that n rises. Its graph is a line with slope 10 that starts at 25.