Solve y=f(x-m)+b

$$y = f ( x - m ) + b$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{b-y}{x-m}\text{, }&x\neq m\\f\in \mathrm{R}\text{, }&y=b\text{ and }x=m\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by x-m.

$$y=fx-fm+b$$

Swap sides so that all variable terms are on the left hand side.

$$fx-fm+b=y$$

Subtract b from both sides.

$$fx-fm=y-b$$

Combine all terms containing f.

$$\left(x-m\right)f=y-b$$

Divide both sides by x-m.

$$\frac{\left(x-m\right)f}{x-m}=\frac{y-b}{x-m}$$

Dividing by x-m undoes the multiplication by x-m.

$$f=\frac{y-b}{x-m}$$

Solve for b

$$b=fm+y-fx$$