Example 3: $m =\frac 1 2 ; b = 1: f(x) = \frac 1 2x + 1$
Each arrow passes through a single point, which is labeled $F = [1/2,1]$.
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, $\frac 1 2x + 1$, which corresponds to the linear function's value for the point/number, $x$.