average slope
The average slope is a measurement used in mathematics to determine the average rate of change of a function over a specific interval
The average slope is a measurement used in mathematics to determine the average rate of change of a function over a specific interval. It is calculated by finding the difference in the y-coordinates of two points on a function and dividing it by the difference in the corresponding x-coordinates.
To find the average slope between two points (x1, y1) and (x2, y2), the formula is:
Average slope = (change in y-coordinates) / (change in x-coordinates)
= (y2 – y1) / (x2 – x1)
In other words, the average slope gives us the average rate at which the dependent variable (y) changes for each unit increase in the independent variable (x) within the interval.
For example, if you have a linear equation like y = 2x + 3 and you want to find the average slope between the points (1, 5) and (4, 11), you would calculate it as follows:
Average slope = (11 – 5) / (4 – 1)
= 6 / 3
= 2
This means that, on average, the y-values increase by 2 for every 1 unit increase in x within that interval.
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