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)

Question

(
𝑦
)
successfully baked in x days.(1 point)
Responses

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

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

y=x+6
𝑦
=
𝑥
+
6
y equals x plus 6

y=6x−1

Answer 1

To find a linear function \(y\) that represents the number of muffins baked in \(x\) days, we start by analyzing the data given:

• Day 1: 5 muffins
• Day 2: 11 muffins
• Day 3: 17 muffins

We can note the number of muffins baked over each day:

• From Day 1 to Day 2: 11 - 5 = 6 muffins
• From Day 2 to Day 3: 17 - 11 = 6 muffins

This consistent increase of 6 muffins per day suggests a linear relationship.

Let’s define the linear function in the form \(y = mx + b\), where:

• \(m\) is the slope (the change in muffins per day),
• \(b\) is the y-intercept (the number of muffins at Day 0).

From our data:

• Slope \(m = 6\) (they bake 6 more muffins each subsequent day).

Now, to find the y-intercept \(b\), we can use one of our known points. Let's use Day 1 where \(x = 1\) and \(y = 5\): \[ 5 = 6(1) + b \] \[ 5 = 6 + b \] \[ b = 5 - 6 = -1 \]

Putting it all together, the linear function is: \[ y = 6x - 1 \]

Thus, the correct response is: y = 6x - 1.