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

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Answer 1 · 2016-10-05T07:19:23

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.