Question

Alex and Jesse are baking muffins. On day one, they baked five muffins, on day two, they baked 11 muffins, and on day three, they baked 17 muffins. Write a linear function to represent the number of muffins (y)
successfully baked in x days.(1 point)
Responses

y=16x−1
y equals Start Fraction 1 over 6 End Fraction x minus 1

y=6x−1
y equals 6 x minus 1

y=6x+1
y equals 6 x plus 1

y=x+6

Answer 1

To establish a linear function \( y = mx + b \) that represents the number of muffins baked over a given number of days, we can look for the slope (\( m \)) and y-intercept (\( b \)).

From the data provided:
- On day 1 (\( x = 1 \)), \( y = 5 \)
- On day 2 (\( x = 2 \)), \( y = 11 \)
- On day 3 (\( x = 3 \)), \( y = 17 \)

First, let's calculate the slope (\( m \)) using the change in \( y \) over the change in \( x \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11 - 5}{2 - 1} = \frac{6}{1} = 6
\]

We can verify this slope with another pair of points:

\[
m = \frac{17 - 11}{3 - 2} = \frac{6}{1} = 6
\]

Now that we have the slope \( m = 6 \), we can use one of the points to find the y-intercept \( b \). Using the point (1, 5):

\[
y = 6x + b
\]
\[
5 = 6(1) + b
\]
\[
5 = 6 + b
\]
\[
b = 5 - 6 = -1
\]

Now we have \( m = 6 \) and \( b = -1 \), so the linear function is:

\[
y = 6x - 1
\]

Thus, the correct option is:

**y = 6x - 1**.