Which situation represents a proportional relationship?

question 4 options:

a. the cost of purchasing a basket of apples for $1.25 per pound plus $5.00 for the basket

b. the cost of purchasing bananas for $5.00 per box of bananas with the delivery charge of $3.00

c. the cost of purchasing limes for $ 0.65 per pound with a coupon for $1.00 off the total cost

d. the cost of purchasing avocados for $1.75 per pound plus a shipping fee of $0.16 per pound.

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 , where, is the unit rate and is the fixed value (constant).

For a proportional relationship, the value of and thus it is of the form

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

Option A:

Given:

Unit rate of purchasing a basket of apples,

Fixed price for the basket,

Since, , therefore, it is not a proportional relationship.

Option B:

Given:

Unit rate of purchasing a banana,

Fixed price for the box,

Since, , therefore, it is not a proportional relationship.

Option C:

Given:

Unit rate of purchasing a lime,

Discount from total cost,

Since, , therefore, it is not a proportional relationship.

Option D:

Given:

Unit rate of purchasing an avocado =

Unit rate of shipping =

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

Total cost of avocados per pound,

There is no fixed cost on this. So,

Since, , therefore, it is a proportional relationship.

Therefore, the correct option is D.

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.