Question

Suppose that (x1, y1) and (x2, y2) are two points on a linear function. Write the formula to find the function’s rate of change for the interval [x1, x2].

Answer 1

The rate of change for a linear function on the interval [x1, x2] is the slope of the line m, calculated by dividing the difference in y-values by the difference in x-values: m = (y2 - y1) / (x2 - x1).

Step-by-step explanation:

To find the rate of change of a linear function for the interval [x1, x2], we need to calculate the slope of the line connecting the points (x1, y1) and (x2, y2). This is done using the formula:

m = (y2 - y1) / (x2 - x1)

where m represents the slope, which is the ratio between the change in y-values (rise) and the change in x-values (run). When graphing the function, if you plotted these two points, you'd be able to draw a straight line between them, and by finding the slope, you determine how steep the line is. The slope, or rate of change, indicates how much y increases or decreases for each unit increase in x. This rate of change is constant along the entire length of a straight line.

Answer 2

This is just the slope.
(y2 - y1)/(x2 - x1)