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 [tex]y=mx+b[/tex], where, [tex]m[/tex] is the unit rate and [tex]b[/tex] is the fixed value (constant).
For a proportional relationship, the value of [tex]b=0[/tex] and thus it is of the form [tex]y=mx[/tex]
Let us check each option and express it in the form above.
Option A:
Given:
Unit rate of purchasing a basket of apples, [tex]m=\$ 1.25[/tex]
Fixed price for the basket, [tex]b=\$ 5[/tex]
Since, [tex]b \ne 0[/tex], therefore, it is not a proportional relationship.
Option B:
Given:
Unit rate of purchasing a banana, [tex]m=\$ 5[/tex]
Fixed price for the box, [tex]b=\$ 3[/tex]
Since, [tex]b \ne 0[/tex], therefore, it is not a proportional relationship.
Option C:
Given:
Unit rate of purchasing a lime, [tex]m=\$ 0.65[/tex]
Discount from total cost, [tex]b=\$ 1[/tex]
Since, [tex]b \ne 0[/tex], therefore, it is not a proportional relationship.
Option D:
Given:
Unit rate of purchasing an avocado = [tex]\$ 1.75[/tex]
Unit rate of shipping = [tex] \$ 0.16[/tex]
Therefore, total cost per pound is the sum of the unit rates of purchasing and shipping. So,
Total cost of avocados per pound, [tex]m=1.75+0.16=\$ 1.91[/tex]
There is no fixed cost on this. So, [tex]b=0[/tex]
Since, [tex]b = 0[/tex], therefore, it is a proportional relationship.
Therefore, the correct option is D.
