Example LF.2.2: $m  = 2; b = 1: f (x) = 2x + 1$

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, $2x + 1$, which corresponds to the linear function's value for $x$.

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Notice that for each unit increase in $x$ there is a corresponding increase by 2 units in the  value of $f(x)$.
Thus there is a constant rate of change for $f$, precisely $2$,  the value of $m$.