Example 4: $m = 0; b = 1:  f(x) = 0 x + 1$

Each arrow passes through a single point, which is labeled $F = [0,1]$.
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, $f(x)=1$, which corresponds to the linear function's value for the point/number, $x$.