Question

The relationship between a distance in yards (y) and the same distance in miles (m) is described by the equation y=1760m. Is there a proportional relationship between a measurement in yards and a measurement in miles for the same distance? Explain why or why not

Answer 1

Yes. There exist a direct proportionality, since a change in one variable leads to a direct change in the other variable and exist a constant ratio between them.

Explanation:

The condition of direct proportionality mean the existence of the following relationship:

`y \propto m`

`y = k\cdot m`

Where k is a constant of proportionality, the suggested formula observes every characteristic of the direct proportionality. (k = 1760)

Answer 2

y ∝ m and 1760 is a constant of proportionality.

Explanation:

The relation between a distance in the yards (y) and the same distance in miles (m) is described by the equation y = 1760m.

So, the graph of the above equation passes through the origin(0,0) and it will be a straight line with a constant slope of 1760.

Therefore, a measurement in yards and a measurement in miles are in the relation of proportionality for the same distance.

Hence, y ∝ m and 1760 is a constant of proportionality. (Answer)