Question

\left(1,\ 5.75\right) \left(2,\ 8.5\right) \left(3,\ 11.25\right) \left(4,\ 14\right) \left(5,\ 16.75\right) \left(10,\ 30.5\right) What function matches the dotted line on the left?

(fill in the slope m and y-intercept b)



Remember: A bacon egg & cheese sandwich from them costs $2.75 each with a $3.00 delivery fee.



You will know you are correct when your line turns SOLID PURPLE!

Answer 1

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.

1. Let \(x\) be the number of sandwiches ordered.
2. 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:

- For \(x = 1\):
\[
C = 2.75(1) + 3 = 5.75 \quad \text{(matches)}
\]

- For \(x = 2\):
\[
C = 2.75(2) + 3 = 8.50 \quad \text{(matches)}
\]

- For \(x = 3\):
\[
C = 2.75(3) + 3 = 11.25 \quad \text{(matches)}
\]

- For \(x = 4\):
\[
C = 2.75(4) + 3 = 14.00 \quad \text{(matches)}
\]

- For \(x = 5\):
\[
C = 2.75(5) + 3 = 16.75 \quad \text{(matches)}
\]

- 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.