Average Rate of Change

The Average Rate of Change (ARC) is a measure of how much a quantity changes on average over a specific interval. It is calculated using the formula: ARC = (y2 - y1) / (x2 - x1).

The slope of a line is calculated using the formula: slope (m) = (y2 - y1) / (x2 - x1).

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

The slope of a horizontal line is 0, indicating no change in the y-value as the x-value changes.

The slope of a vertical line is undefined, as the x-value does not change while the y-value does.

To find the average rate of change, use the formula: ARC = (f(x2) - f(x1)) / (x2 - x1) for the function f.

The slope can represent rates of change, such as speed, growth, or decline in various real-world scenarios.

The average rate of change is (48 - 40) / (5 - 3) = 8 / 2 = 4 inches per year.