Final answer:
The average rate of change between the points (-1, 4/3) and (0, 2) is found by taking the difference in their y-values (change in y) over the difference in their x-values (change in x), which yields an average rate of change of 2/3, corresponding to option A.
Step-by-step explanation:
The question asks us to determine the average rate of change between the two points (-1, 4/3) and (0, 2). To find this, we can use the formula of the slope of the line connecting these two points, which is given by:
\(\text{Average Rate of Change} = \frac{\text{Change in y}}{\text{Change in x}} = \frac{y_2 - y_1}{x_2 - x_1}\)
Plugging in our points, we get:
\(\frac{2 - \frac{4}{3}}{0 - (-1)} = \frac{\frac{6}{3} - \frac{4}{3}}{1} = \frac{\frac{2}{3}}{1} = \frac{2}{3}\)
Thus, the average rate of change is 2/3, which corresponds to option A.