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Slope is a rate of change in the dependent variable for a given change of the independent variable of a function.

The average slope, or slope of the secant line between x1 and x2, can be computed using the formula:

$ \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} $.

When a linear equation (with no powers other than one and zero) is written in slope-intercept form ($ y = mx + b $), the slope is $ m $, the coefficient of $ x $.

To find the instantaneous slope of a function, or the slope of the tangent line at x0, the limit as x approaches x0 can be taken.

$ \lim_{ \Delta x \to 0} \frac{\Delta y}{\Delta x} = \lim_{ x \to x_0} \frac{f(x) - f(x_0)}{x - x_0} $

This can be extended to every point on a curve by the formula

$ \lim_{ h \to 0} \frac{f(x + h) - f(x)}{h} $

which is the definition of the derivative of f(x).