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 Average Rate of Change ARC The change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value divided by the change in the x-value for two distinct points on the graph. Any of the following formulas can be used. ARC = average rate of change = $$\frac{{\Delta y}}{{\Delta x}} = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{f\left( {{x_2}} \right) - f\left( {{x_1}} \right)}}{{{x_2} - {x_1}}} = \frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}$$ Note: This is the same thing as the slope of the secant line of a curve.     See also Instantaneous rate of change, mean value theorem