Final answer:
The average rate of change is calculated using the formula Δy/Δx and requires substituting the final and initial x and y values of two points into the equation. Only option a) Δy/Δx correctly represents this rate of change.
Step-by-step explanation:
The student appears to be asking how to find the average rate of change. In mathematics, the average rate of change is represented by the slope of the secant line connecting two points on a graph of a function. The formula to find the average rate of change is Δy/Δx, where Δy represents the change in the y-values, and Δx represents the change in the x-values. To calculate it, one must substitute the x and y values of the chosen points into the equation and use the final value minus the initial value for both Δy and Δx. Formula b) Δx/Δy is incorrect as it inverts the order of the variables, and formulas c) (Δx * Δy)/(Δx + Δy) and d) Δy/Δx + Δx/Δy do not represent the average rate of change in a function. The correct interpretation and calculation of the average rate of change are essential in various applications, including solving for displacement (Δx) and final position (x) from average velocity when acceleration (a) is constant.