Solve for \(\displaystyle m\).

\(\displaystyle y = mx + b\)

\(\displaystyle \dfrac{y}{x} = \dfrac{mx}{x} + \dfrac{b}{x}\)

\(\displaystyle \dfrac{y}{x} = m + \dfrac{b}{x}\)

\(\displaystyle -m = -\dfrac{y}{x} + \dfrac{b}{x}\)

\(\displaystyle \dfrac{-m}{-1} = \dfrac{-\dfrac{y}{x}}{-1} + \dfrac{\dfrac{b}{x}}{-1}\)

\(\displaystyle m = \dfrac{y}{x} - \dfrac{b}{x}\)

or

\(\displaystyle m = \dfrac{1}{x}[y - b]\)