Question

The Picture and Sound Electronics Store has hired Nathan to work in the warehouse. He uses a pulley with a hand crank to lift heavy boxes. Nathan lifts a box 1 foot each time he turns the crank. Is there a proportional relationship between the number of times Nathan turns the crank to lift a box, x, and the height the box is lifted, y?

1) Yes
2) No

Answer 1

Nathan has a proportional relationship between the number of crank turns and the height the box is lifted, as the box is raised 1 foot per crank turn.

Step-by-step explanation:

There is indeed a proportional relationship between the number of times Nathan turns the crank to lift a box, x, and the height the box is lifted, y. Since Nathan lifts the box 1 foot with each turn of the crank, we can express this relationship with the equation y = x. This means for every turn of the crank (x), the height (y) increases by 1 foot proportionally.

In terms of proportional relationships, two quantities are proportional if they maintain the same ratio. Here, that ratio is 1 foot per crank turn, which is consistent no matter how many times the crank is turned. Furthermore, if we were to graph this relationship, we would see a straight line passing through the origin (0,0), further confirming that the relationship is proportional.