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How to Find the Average Slope of a Function

Finding the average slope of a function is a common calculation done in algebra. You can calculate the average slope for any algebraic function, and over any two points of that function. This is an important point of this calculation. The average slope of the function can be very different depending on the points selected. There is no equation in algebra that allows you to calculate the average slope of the entire function, though there are methods for this in calculus.

Things You'll Need

  • Pencil
  • Paper
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Instructions

    • 1

      Write down the equation for which you'd like to calculate the average slope. For example, let's use f(x)=x²+2x-1.

    • 2

      Write the formula for average slope on your paper. It is the following:

      A= (f(x) - f(a)) / (x - a)

      A stands for the average slope. (x-a) stands for the change in the input, and (f(x) - f(a)) stands for the change in output, the f representing the function.

    • 3

      Choose values for x and a. Depending on the equation, the points that you choose can have a great effect on the calculation's outcome. The points you choose determine the section of the graph that you are calculating the slope of. In our example, let's choose x=3 and a=0.

    • 4

      Plug a and x first into the function to calculate f(x) and f(a). In our example, this gives us f(x)=3² + 2(3) - 1=14 and f(a)=0² + 2(0) - 1= -1.

    • 5

      Plug those answers into the average slope equation. This gives us A = (14 - (-1)) / (3 - 0) = 5. So the average slope of the equation between the two points is 5.

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