Question

the graph shows the weight of a pitcher, y, as a function of the number of cups of water in the pitcher, x. the initial value is 12. it represents the weight in ounces of the empty pitcher. what is the rate of change of the function? rate of change = \frac{change in y - values}{change in x - values}=\frac{36 - 12}{3 - 0}=8 describe the rate of change of the function. the rate of change is 8. it represents the weight in ounces of?

Explanation:

Step1: Recall rate - of - change formula

The rate of change of a linear function is given by $\text{rate of change}=\frac{\text{change in }y\text{-values}}{\text{change in }x\text{-values}}$.

Step2: Identify two points

We can use the points $(0, 12)$ (when $x = 0$, $y=12$ which is the initial value) and $(3,36)$ from the graph.

Step3: Calculate rate of change

$\text{rate of change}=\frac{36 - 12}{3-0}=\frac{24}{3}=8$.

Step4: Interpret the rate of change

The rate of change 8 represents the weight in ounces of one cup of water. Since the weight of the pitcher changes by 8 ounces for each additional cup of water, 8 ounces is the weight of one cup of water.

Answer:

The rate of change is 8. It represents the weight in ounces of one cup of water.