Question

mr. willbury buys a bag of granola for snacks. the graph shows the total weight of the bag of granola, y, as a function of the number of cups he eats, x. use the graph to describe the function. the initial value is 14. it represents the weight of the bag when it is full. the total weight of the bag? when mr. willbury eats the granola. that means the rate of change is? .

Explanation:

Step1: Analyze the graph

The graph shows a linear relationship between the total weight of the bag \(y\) and the number of cups eaten \(x\). Since the line is going downwards, the total weight of the bag decreases when Mr. Willbury eats the granola.

Step2: Calculate the rate of change

The rate of change (slope \(m\)) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
We can take two points from the graph: \((0,14)\) and \((3.5,0)\)

$$m=\frac{0 - 14}{3.5-0}=\frac{- 14}{3.5}=-4$$

Answer:

The total weight of the bag decreases when Mr. Willbury eats the granola. That means the rate of change is \(-4\)