To identify the function that fits the given points and represents the cost of the bacon egg & cheese sandwiches, let’s first analyze the points provided. The points are:
\[ (1, 5.75), (2, 8.5), (3, 11.25), (4, 14), (5, 16.75), (10, 30.5) \]
We can begin by identifying the cost structure based on your description. Each sandwich costs $2.75, and there is a $3.00 delivery fee.
- Let \(x\) be the number of sandwiches ordered.
- The total cost \(C\) can be expressed as: \[ C = 2.75x + 3 \]
Here, \(m = 2.75\) (the slope) and \(b = 3\) (the y-intercept).
Now, we can verify that this function matches the given points:
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For \(x = 1\): \[ C = 2.75(1) + 3 = 5.75 \quad \text{(matches)} \]
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For \(x = 2\): \[ C = 2.75(2) + 3 = 8.50 \quad \text{(matches)} \]
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For \(x = 3\): \[ C = 2.75(3) + 3 = 11.25 \quad \text{(matches)} \]
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For \(x = 4\): \[ C = 2.75(4) + 3 = 14.00 \quad \text{(matches)} \]
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For \(x = 5\): \[ C = 2.75(5) + 3 = 16.75 \quad \text{(matches)} \]
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For \(x = 10\): \[ C = 2.75(10) + 3 = 30.5 \quad \text{(matches)} \]
Since this linear function perfectly fits all the provided data points, we have confirmed the slope and y-intercept.
Thus, the answer is:
Slope \(m = 2.75\) and y-intercept \(b = 3\).
Your function \(C(x) = 2.75x + 3\) should result in a solid purple line when plotted correctly.