Example 2: $m = 2; b = 1: f(x) = 2x + 1$
Each arrow passes through a single point, which is labeled
$F =
[2,1]$.
The point $F$ completely determines the function $f$.
Given a point / number, $x$, on the source line,
there is a unique arrow passing through $F$
meeting the target line at a unique point / number, $2x + 1$, which
corresponds to the linear function's value for the point/number,
$x$.