a magician charges $50.00 for a visit and an additional $7.50 for each hour he preforms. the function rule c + 7.50h + 50.00 describes the relationship between the number of hours h and the total cost of the visit c. if the magician will only visit a maximum of 8 hours, what is a reasonable graph of the function rule?
To graph the function rule c = 7.50h + 50.00, we can consider the possible values of h and find the corresponding values of c.
Let's select a few values for h, such as 0, 2, 4, 6, and 8, and calculate the respective values of c:
For h = 0: c = 7.50(0) + 50.00 = 50.00
For h = 2: c = 7.50(2) + 50.00 = 65.00
For h = 4: c = 7.50(4) + 50.00 = 80.00
For h = 6: c = 7.50(6) + 50.00 = 95.00
For h = 8: c = 7.50(8) + 50.00 = 110.00
Plotting these values on a graph, with h on the x-axis and c on the y-axis, we get a straight line that passes through the points (0, 50.00), (2, 65.00), (4, 80.00), (6, 95.00), and (8, 110.00). The line has a positive slope of 7.50, indicating that as the number of hours increases, the total cost also increases.
Since the magician will only visit a maximum of 8 hours, it makes sense to only consider values up to h = 8. Thus, the graph would look something like this:
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120 | o
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100 | o
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80 | o
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60 | o
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40 | o
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0 4 8
Number of Hours (h)