To determine the most appropriate graph for the situation described (where the total rental cost is composed of a fixed price of $100 plus $10 for each guest), we need to analyze the relationship between the number of guests and the total rental cost.
The total cost can be represented by the equation: \[ \text{Total Cost} = 100 + 10 \times \text{Number of Guests} \]
Given this equation, the following claims can be made:
- If we have the number of guests on the x-axis, the cost on the y-axis will increase linearly, starting from $100 when there are 0 guests.
- The cost increases by $10 for every additional guest, which means the y-axis should reflect smaller intervals (since costs can rise quickly for larger numbers of guests).
Now, let's evaluate the options:
A. Total Rental Cost in dollars (interval of 100) on x-axis, Number of Guests (interval of 10) on y-axis: This does not capture the cost well because the cost won't reach hundreds until you have many guests—making the scale inappropriate for smaller numbers of guests.
B. Number of Guests (interval of 1) on x-axis, Total Rental Cost in dollars (interval of 100) on y-axis: While the x-axis is appropriately scaled, the y-axis is not effective, as the cost will not reach $100 until there are 10 guests, making the increments too large for typical usage.
C. Number of Guests (interval of 10) on x-axis, Total Rental Cost in dollars (interval of 10) on y-axis: This does not work well because the x-axis will represent too large increments for guests, which are typically counted more granularly (1, 2, 3, etc.).
D. Number of Guests (interval of 10) on the x-axis and Total Rental Cost in dollars (interval of 100) on y-axis: This is the least effective because again, the x-axis intervals are too large for typical scenarios involving guests.
Hence, Option B is the best choice since it has the number of guests in smaller increments on the x-axis, even though the cost intervals on the y-axis are too broad. The most appropriate graph for this situation is:
B. A graph shows the number of guests with an interval of 1 unit on the x-axis and the total rental cost with an interval of 100 units on the y-axis.
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