# How is growth related to the slope of a linear function?

Oct 5, 2016

See explanation.

#### Explanation:

If y = mx + c, a linear function, its graph is a straight line.

The constant slope of the line is $y ' = \frac{\mathrm{dy}}{\mathrm{dx}} = m$

Verbally, y' is the rate at which y changes with respect to x.

It is the limit $\Delta x \to 0$ of $\frac{\Delta y}{\Delta x}$.

If y increases as x increases, both $\Delta y \mathmr{and} \Delta x$ will be

positive, and so, the limit y' will be positive. So, locally it is growth.

If..y' is negative, it is locally decay. If y'=0, it is locally neither.