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. is the rate of change positive or negative? the line slants upward from left to right. that means the rate of change is positive. how can you find the rate of change? rate of change = ? / ?

Explanation:

Step1: Recall rate - of - change formula

The rate of change (slope) of a linear function is given by the formula $m=\frac{\text{change in }y}{\text{change in }x}=\frac{y_2 - y_1}{x_2 - x_1}$. In the context of the problem, the rate of change of the weight of the pitcher (y) with respect to the number of cups of water (x) is found by taking the difference in weights divided by the difference in the number of cups.

Answer:

rate of change $=\frac{\text{change in weight of pitcher}}{\text{change in number of cups}}$