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) \\(\bigcirc\\) \\(y = x + 6\\) \\(\bigcirc\\) \\(y = 6x - 1\\) \\(\bigcirc\\) \\(y = 6x + 1\\) \\(\bigcirc\\) \\(y = \frac{1}{6}x - 1\\)

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((1,5)\) and \((2,11)\):
\(m=\frac{11 - 5}{2 - 1}=\frac{6}{1}=6\).

Step2: Use point - slope form \(y - y_1=m(x - x_1)\)

Using point \((1,5)\) and \(m = 6\):
\(y - 5=6(x - 1)\)
Expand: \(y - 5=6x - 6\)
Add 5 to both sides: \(y=6x - 1\).

Step3: Verify with \(x = 3\)

Substitute \(x = 3\) into \(y = 6x - 1\):
\(y=6(3)-1=18 - 1 = 17\), which matches the given data.

Answer:

\(y = 6x - 1\) (corresponding to the option \(y = 6x - 1\))