The linear function \( y = 145 + 30x \) represents the total cost \( y \) of an airline ticket based on the number of checked bags \( x \). Here's the interpretation of the terms and coefficients in the equation:
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Intercept (145):
- The term \( 145 \) represents the base cost of the airline ticket without any checked bags. This is the fixed cost you pay when you purchase the ticket, regardless of whether you check any bags.
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Slope (30):
- The coefficient \( 30 \) indicates the additional cost incurred for each checked bag. Specifically, it means that for every checked bag added (increment of \( x \) by 1), the total cost \( y \) increases by $30.
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Variable (x):
- The variable \( x \) represents the number of checked bags. Since the problem states that at most 5 bags can be checked, \( x \) can take on values from 0 to 5.
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Total Cost (y):
- The total cost \( y \) is a function of the number of checked bags. As \( x \) increases, \( y \) will adjust accordingly based on the equation, showing how the total ticket price changes with the number of bags checked.
To summarize, if you check 0 bags, the cost is $145. If you check 1 bag, the cost increases to \( 145 + 30(1) = 175 \), for 2 bags, \( 145 + 30(2) = 205 \), and so on, up to the maximum of 5 bags.
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