Consider the linear function $f(x) = mx + b$.

When $m = 0$, the function  has the same constant value $b$ for any $x$. "The function $f$ is a constant function."
When $m \ne 0$ , the values of the  linear function $f$ vary in predictable ways depending on whether $m>0$ or $m<0$.
This is apparent by reviewing the mapping diagrams along with the graphs in some of our previous examples.
But first we define the key concepts: increasing and decreasing. 

Definition ID Increasing/Decreasing

Review of two previous examples.
Notice how the graph and mapping diagram visualize the fact that for linear functions, if $m >0$ then $f$ is an increasing function while if $m<0$ then $f$ is a decreasing function ( and the converses are also true for linear functions.)

Example LF.4.1 : $m =-2; b = 1: f(x) = -2x + 1$
Example LF.4.2 : $m = 2; b = 1:  f(x) = 2x + 1$

You can use this next dynamic example to investigate visually the effects of the linear coefficient and the constant term simultaneously on whether the function is increasing or decreasing in a mapping diagram  of $f$ and the line in the graph of $f$.

Example LF.DID.0 Dynamic Visualization of Increasing and Decreasing for Linear Functions: Graphs, and Mapping Diagrams

Reminder: If $m >0$ then $f$ is an increasing function while if $m<0$ then $f$ is a decreasing function.
The value of $b$ does not effect whether $f$ is increasing or decreasing.