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

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

GPT-4o mini · Answer

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**.