Question

Threads Garage is a thrift store that sells clothing by the pound. Customers fill a plastic bag with their desired amount of clothing. Then, the bag is then weighed at checkout to calculate the cost. There is a linear relationship between the weight of a bag of clothing, in pounds, and its cost. 3 6 9 12 15 18 21 24 $3 $6 $9 $12 $15 $18 $21 $24 x y Weight (pounds) Cost ($) Describe the rate of change for this relationship. The cost of a bag of clothing increases increases decreases by $0.40 $0.50 $2.00 $2.50 $3.00 $9.00 per pound.

Answer 1

To determine the rate of change for the relationship between the weight of a bag of clothing (x) and its cost (y), we can analyze the provided information.

From your data, we can observe the following pairs:

• At 3 pounds, the cost is $3
• At 6 pounds, the cost is $6
• At 9 pounds, the cost is $9
• At 12 pounds, the cost is $12
• At 15 pounds, the cost is $15
• At 18 pounds, the cost is $18
• At 21 pounds, the cost is $21
• At 24 pounds, the cost is $24

The relationship is linear, as the cost increases by a constant amount for each increase in weight.

To find the rate of change (slope) in this linear relationship, we can look at the change in cost divided by the change in weight.

From the data, we see:

• As the weight increases from 3 pounds to 6 pounds (an increase of 3 pounds), the cost increases from $3 to $6 (an increase of $3).
• This pattern continues consistently through the data.

Calculating the slope:

• Cost change: \( \Delta y = 6 - 3 = 3 \) dollars
• Weight change: \( \Delta x = 6 - 3 = 3 \) pounds

Thus, the rate of change (slope) is:

\[ \text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{3 \text{ dollars}}{3 \text{ pounds}} = 1 \text{ dollar per pound} \]

So, the cost of a bag of clothing increases by $1.00 per pound.