In the equation \( c = 18 + 4x \), the term \( 4x \) represents a linear relationship between two variables. Here, \( c \) denotes a total cost, and \( x \) denotes the number of items (for example, books or paperbacks).
In this context:
- The constant term \( 18 \) represents a fixed cost, which could be interpreted as an initial fee or base cost associated with purchasing or borrowing the books.
- The coefficient \( 4 \) indicates a variable cost that is dependent on how many items (books) are involved.
Interpretation of Coefficient:
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Statement 1: "You can spend $4 per paperback at the public library."
- Correct Interpretation: This statement correctly interprets the coefficient \( 4 \) as the cost associated with each paperback (hence it's the variable cost incurred for each additional book).
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Statement 2: "10 minutes per book at the public library."
- Incorrect Interpretation: This statement does not correspond with the meaning of the coefficient \( 4 \) in the context of the equation, as it relates to a time duration rather than a monetary cost.
Conclusion:
Only Statement 1 could be a correct interpretation of the coefficient \( 4 \) in the equation \( c = 18 + 4x \).