Chapter 4 - An Introduction to Functions - 4-1 Using Graphs to Relate Two Quantities - Practice and Problem-Solving Exercises - Page 238: 16

The relationship between the number of turns of Gear A with number of turns with Gear b is y=1/2x The turns of Gear b is independent variable and Gear A is dependent variable. The table and the graph of this relationship is shown in a screenshot. In order to move the Gear A once, you have to move the Gear B twice.

Gear B is independent variable because you have to move the gear B in order to move the gear A, and thus Gear A is affected by the movement of Gear B. The equation is y=1/2x because for every turn of gear B, the gear A is turned half. You need to turn the Gear B twice because gear B makes a complete round after 8 turns and Gear A makes a completer round after 16 turns.