Ludwik,
You are correct in that y=m*x+b has a linear relation between y
and x but is not proportional to because if you double x, you get twice
y plus b. In strict semantics they are not equivalent. However, I can
see people using them interchanging them like velocity and speed. I
could almost go along with it if b is very small because then y is
almost proportional to x. Guess you have ot clarify what almost means.