Question

The Picture and Sound electronics store has hired Tanner to work in the warehouse. He uses a pulley with a hand crank to lift heavy boxes.

There is a proportional relationship between the number of times Tanner turns the crank to lift a box, x, and the height the box has been lifted (in feet), y.

x (time tanner turns the crank) y(feet)
46 46
61 61
65 65
91 91

What is the constant of proportionality?

Answer 1

In a proportional relationship, the constant of proportionality (\(k\)) is the ratio between the two variables. In this case, the relationship is between the number of times Tanner turns the crank (\(x\)) and the height the box is lifted (\(y\)).

Let's take any pair of values from the given data and find the constant of proportionality:

\[ k = \frac{y}{x} \]

Let's use the first pair (46, 46):

\[ k = \frac{46}{46} = 1 \]

So, the constant of proportionality (\(k\)) is 1 in this case. The relationship between \(x\) and \(y\) is \(y = x\) for the given data.