Line segment graphs are useful when the rate of increase or decrease in a situation changes after a certain point.

### Application

When a furniture seller sells a couch, she earns commission at the rate of 2% on the first \$30000 and 0.9% on the remainder. Calculate the commission earned on sales of:

a) \$15000
b) \$40000

This situation can be illustrated as below:

The maximum commission she can earn from the rate of 2% is 0.02*30000 which is \$600. After earning \$600, she then gets commission at the rate of 0.8% for the remainder.

In part a), the sales have not yet reached the change in commission rate and hence only the 2% rate applies. The seller thus earns:
0.02 * 15000 = \$300

In part b), both rates must be taken into account as it exceeds \$30000. For the first \$30000 of sales, the seller earns \$600 of commission. After that, there is \$10000 of sales to account for. The commission calculated with the remaining amount is at the rate of 0.9%. Thus, she earns an additional 0.009*10000 = \$90. The total commission made from the sale of \$40000 is \$690.