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

1 Answer
Oct 5, 2016

See 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.