Question

mr. baker, the owner of buzz bees bakery, made a large batch of honey-lavender cookie dough. he pulled equal-sized balls of dough from the batch to form the cookies. the amount of dough mr. baker has left depends on how many cookies he has formed. this situation can be modeled as a linear relationship. (chart: x-axis is cookies formed, y-axis is ounces of dough left, line starts at (0,108) and goes down)

Explanation:

Step1: Identify the slope formula

The slope \( m \) of a line is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1,y_1) \) and \( (x_2,y_2) \) are two points on the line.
From the graph, we can take two points: when \( x_1 = 0 \), \( y_1=108 \) (the y - intercept) and when \( x_2 = 12 \), \( y_2 = 84 \).

Step2: Calculate the slope

Substitute the values into the slope formula:
\( m=\frac{84 - 108}{12-0}=\frac{- 24}{12}=- 2 \)
The slope represents the rate of change of dough left with respect to the number of cookies formed. A slope of - 2 means that for each cookie formed, the amount of dough left decreases by 2 ounces.

Step3: Determine the equation of the line

The equation of a line in slope - intercept form is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.
We know that \( m=-2 \) and \( b = 108 \) (from the point \( (0,108) \)), so the equation is \( y=-2x + 108 \).

(If the question was to find the rate of change, for example)

Answer:

The rate of change (slope) is \(-2\) ounces per cookie. This means Mr. Baker uses 2 ounces of dough for each cookie he forms.