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If the equation is of the form y = f(x) where f is some function of the variable x, then

The initial value is found by evaluation f(0): that is, the value of f(x) when x = 0.

The rate of change is the derivative of f(x) with respect to x, written as f'(x). That is the limit (if it exists), as dx tends to 0, of [f(x+dx) - f(x)]/dx.

In the simple case, where f(x) is a linear equation of the form y = mx + c, then f(0) = c and f'(x) = m

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