# Let us find the average rate of change formula

In geometrical terms, the "rate of change" is the slope of the line that joins two specific points. This term is also known as the average rate of change. It is very simple to find the rate of change. For the following drawing we will try to find the average rate of change between the two points marked.

Basically, the average rate of change between the points (4,3) and (6,7) is obtained dividing the change in the y-coordinates and the change in the x-coordinates. We will calculate the slope of the line joining the two points with the formula, m = (y2 – y1)/(x2 – x1). The slope will be m = (7 – 3)/(6 – 4) = 2. To conclude, the process of finding rate of change of the line joining the two points in the graph lead us to the result 2.

Having any two points A(x1,y1) and B(x2,y2) in the co-ordinate plane and δx and δy the changes in x, respectively in y, the difference quotient δy/δx = (y2 – y1)/(x2 - x1) is called the average rate of change of y with respect to x over the interval (x1,y1). The average rate of change could be determined very easily using the average rate of change formula. For finding average rate of change, we use the following formula: Average change = (change in y value)/(change in x value). It is very easy to find the average rate of change of a function using a specific formula for this task. The formula is δy/δx = [f(b)-f(a)]/(b-a). In the upper formula for rate of change, (b - a) represents the change in the input of the function, f(b)-f(a) represents the change in the function f as the input change from a to b. δy/δx is the average rate of change function.

## Let us calculate rate of change

Calculating the rate of change is a very simple task which requires the knowledge of one or a few short formulas. If you find it difficult to remember the formulas, all you have to know in order to calculate the rate of change is that it is nothing else but the ratio between the change in the output value and the change in the input value of a function.

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