How do you solve for b in y = mx + b?

Subtract $\textcolor{red}{m x}$ from each side of the equation to solve for $b$:
$y - \textcolor{red}{m x} = m x - \textcolor{red}{m x} + b$
$y - m x = 0 + b$
$y - m x = b$
$b = y - m x$