Example LF 2.4: $m = 0; b = 1: f (x) = 0*x + 1$
Draw a mapping diagram yourself or use the diagram created with GeoGebra to explore the diagram further.
Given a point / number, $x$, on the source line, there is a unique
arrow meeting the target line at the point / number, $1$,
which corresponds to the linear function's value for $x$.
Notice that for each unit increase in $x$ there is no increase
or decrease in the value of $f(x)$.
Thus there is a constant rate of change for $f$, precisely
$0$, the value of $m$.