The problem asks to solve for $m$ from the equation $y = mx + b$.

Step-by-step solution:

1. Starting with the equation: $y = mx + b$
2. Subtract $b$ from both sides to isolate the term involving $m$: $y - b = mx$
3. Now, divide both sides by $x$ to solve for $m$: $m = \frac{y - b}{x}$

Thus, the correct option is: $m = \frac{y - b}{x}$

Do you want more details or have any questions? Here are some related questions to explore this further:

1. How can we rearrange equations to isolate different variables?
2. What happens when $x = 0$ in the equation $y = mx + b$?
3. What is the geometric interpretation of $m$ in this equation?
4. How does the equation change if $b = 0$?
5. What is the slope-intercept form of a line, and why is it useful?

Tip: When solving equations for a variable, always perform inverse operations to isolate the target variable.