Question

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

Answer 1

See explanation.

Explanation:

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

The constant slope of the line is `y'=(dy)/(dx)=m`

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

It is the limit `Deltax to 0` of `(Deltay)/(Deltax)`.

If y increases as x increases, both `Deltay and Deltax` 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.