Question

Which situation represents a proportional relationship?

Answer 1

Answer:

D. The cost of purchasing avocados for $1.75 per pound plus a shipping fee of $0.16 per pound.

Step-by-step explanation:

A linear relationship is of the form $y=mx+b$, where, $m$ is the unit rate and $b$ is the fixed value (constant).

For a proportional relationship, the value of $b=0$ and thus it is of the form $y=mx$

Let us check each option and express it in the form above.

Option A:

Given:

Unit rate of purchasing a basket of apples, $m=\ 1.25$

Fixed price for the basket, $b=\ 5$

Since, $b \ne 0$, therefore, it is not a proportional relationship.

Option B:

Given:

Unit rate of purchasing a banana, $m=\ 5$

Fixed price for the box, $b=\ 3$

Since, $b \ne 0$, therefore, it is not a proportional relationship.

Option C:

Given:

Unit rate of purchasing a lime, $m=\ 0.65$

Discount from total cost, $b=\ 1$

Since, $b \ne 0$, therefore, it is not a proportional relationship.

Option D:

Given:

Unit rate of purchasing an avocado = $\ 1.75$

Unit rate of shipping = $\ 0.16$

Therefore, total cost per pound is the sum of the unit rates of purchasing and shipping. So,

Total cost of avocados per pound, $m=1.75+0.16=\ 1.91$

There is no fixed cost on this. So, $b=0$

Since, $b = 0$, therefore, it is a proportional relationship.

Therefore, the correct option is D.