To find the rate of change for the cost of a bag of clothing per pound, we can analyze the data provided. We see that as the weight increases, the cost increases linearly.
From the given data points:
- For 3 pounds, the cost is $9.00.
- For 6 pounds, the cost is $15.00.
- For 9 pounds, the cost is $21.00.
- For 12 pounds, the cost is $27.00.
We can calculate the cost per pound:
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For the first data point:
- \( \frac{9.00}{3} = 3.00 \) : This means the cost is $3.00 per pound.
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For the second data point:
- \( \frac{15.00}{6} = 2.50 \) : This means the cost is also $2.50 per pound.
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For the third data point:
- \( \frac{21.00}{9} = 2.33 \) : This means the cost is approximately $2.33 per pound.
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For the fourth data point:
- \( \frac{27.00}{12} = 2.25 \) : This means the cost is approximately $2.25 per pound.
Now we can observe the consistent price per pound across all weights:
Using the first data pair (3 pounds and $9.00) allows us to establish that the cost increases by $3 for each additional pound (since $9 for 3 pounds leads to a linear relationship where each additional pound costs $3). So, the cost per pound is:
\[ \text{Cost per pound} = \frac{Cost}{Weight} = \frac{$3.00}{1 \text{ pound}} \]
Therefore, the rate of change for this relationship is:
The cost of a bag of clothing is $3.00 per pound.
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