Banquet Hall Rental Fee and Cost Equation
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Caden and his older sisters are planning a twenty-fifth wedding anniversary party for their parents. The banquet hall they plan to use charges a flat rental fee plus a catering fee for each guest. The graph shows the total fees as a function of the numbers of guests. What is the banquet hall rental fee, excluding food? $...$ Complete the equation to represent the relationship between the total fees, T, and the number of guests, g.
This question includes visual content: A coordinate plane plot with 'Number of guests' on the horizontal axis (g) and 'Total fees ($)' on the vertical axis (T). The x-axis is marked from 10 to 100 in increments of 10. The y-axis is marked from 100 to 1,000 in increments of 100. A straight red line starts at (0, 200) on the y-axis and passes through (40, 800), representing the cost function T(g).
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In this problem, we need to find the banquet hall's flat rental fee and the equation for the total cost based on the number of guests. Let's look at the graph provided.
Banquet Hall Fees Analysis
The total fee consists of a flat rental fee plus a catering fee per guest. This is a linear relationship in the form T equals slope times g plus intercept.
The flat rental fee is the fixed cost when there are zero guests. On the graph, this corresponds to the vertical intercept.
Looking at the y-axis, we can see that when g is zero, the total fee T is two hundred dollars. This is our flat rental fee.
Now, let's find the catering fee per guest, which is the slope of the line. We can pick two points on the line to calculate the rise over run.
Let's use the point zero comma two hundred and another clear point, like fifty comma one thousand, as seen on the graph.
Points: (0, 200) and (50, 1000)
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