Which pair of quantities is least likely to be directly proportional?

a. hours worked and money earned

b. distance and time when speed is constant

c. area and side length of a square

d. total cost and the number of hats purchased

D.Total cost and the number of hats purchased

Step-by-step explanation:

When two variables are directly proportional, they increase or decrease at the same rate. This can be represented by the formula

Y = KX

where Y and X are the variables and K represents a constant.

If the pairs can be written in this form then they are directly proportional. In other words, if you can identify the constant K for each pair then they are directly proportional.

Lets take each pair.

A.Hours worked and money earned

This most likely would have a constant K which is equal to the amount of money paid per hour. This amount is usually a fixed amount.

B.Distance and time when speed is constant

Already the constant K is indicated as speed

C.Area and side length of a square

This could be a bit tricky as some people might see the relationship as

Area = The square of the side length

However, for this case the constant K is also taken to be equal to the side length.

Therefore, this can be written as

Area = K × Side length          (where K is the length of the square)

D.Total cost and the number of hats purchased

This is a case of replicating option B without indicating a constant. If the option included "all hats are the same price" then we have a constant for the pairs, unfortunately it didn't and that makes it least likely to be directly proportional.

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