Example 1: $m  = -2; b = 1: f (x) = -2x + 1$

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, $x$.