Solve ry-y_{0}=B/A(x-x_{0})

$$r y - y _ { 0 } = \frac { B } { A } ( x - x _ { 0 } )$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=-\frac{A\left(y_{0}-ry\right)}{x-x_{0}}\text{, }&A\neq 0\text{ and }x\neq x_{0}\\B\in \mathrm{C}\text{, }&y_{0}=ry\text{ and }x=x_{0}\text{ and }A\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by A.

$$ryA-y_{0}A=B\left(x-x_{0}\right)$$

Use the distributive property to multiply B by x-x_{0}.

$$ryA-y_{0}A=Bx-Bx_{0}$$

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

$$Bx-Bx_{0}=ryA-y_{0}A$$

Combine all terms containing B.

$$\left(x-x_{0}\right)B=ryA-y_{0}A$$

The equation is in standard form.

$$\left(x-x_{0}\right)B=Ary-Ay_{0}$$

Divide both sides by x-x_{0}.

$$\frac{\left(x-x_{0}\right)B}{x-x_{0}}=\frac{A\left(ry-y_{0}\right)}{x-x_{0}}$$

Dividing by x-x_{0} undoes the multiplication by x-x_{0}.

$$B=\frac{A\left(ry-y_{0}\right)}{x-x_{0}}$$

Solve for A

$$\left\{\begin{matrix}A=-\frac{B\left(x-x_{0}\right)}{y_{0}-ry}\text{, }&x\neq x_{0}\text{ and }B\neq 0\text{ and }\left(y_{0}\neq 0\text{ or }y\neq 0\right)\text{ and }\left(y=0\text{ or }r\neq \frac{y_{0}}{y}\right)\text{ and }\left(r\neq 0\text{ or }y_{0}\neq 0\right)\text{ and }y_{0}\neq ry\\A\neq 0\text{, }&y_{0}=ry\text{ and }\left(x=x_{0}\text{ or }B=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable A cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by A.

$$ryA-y_{0}A=B\left(x-x_{0}\right)$$

Use the distributive property to multiply B by x-x_{0}.

$$ryA-y_{0}A=Bx-Bx_{0}$$

Combine all terms containing A.

$$\left(ry-y_{0}\right)A=Bx-Bx_{0}$$

Divide both sides by ry-y_{0}.

$$\frac{\left(ry-y_{0}\right)A}{ry-y_{0}}=\frac{B\left(x-x_{0}\right)}{ry-y_{0}}$$

Dividing by ry-y_{0} undoes the multiplication by ry-y_{0}.

$$A=\frac{B\left(x-x_{0}\right)}{ry-y_{0}}$$

Variable A cannot be equal to 0.

$$A=\frac{B\left(x-x_{0}\right)}{ry-y_{0}}\text{, }A\neq 0$$

Solve for B

$$\left\{\begin{matrix}B=-\frac{A\left(y_{0}-ry\right)}{x-x_{0}}\text{, }&A\neq 0\text{ and }x\neq x_{0}\\B\in \mathrm{R}\text{, }&y_{0}=ry\text{ and }x=x_{0}\text{ and }A\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by A.

$$ryA-y_{0}A=B\left(x-x_{0}\right)$$

Use the distributive property to multiply B by x-x_{0}.

$$ryA-y_{0}A=Bx-Bx_{0}$$

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

$$Bx-Bx_{0}=ryA-y_{0}A$$

Combine all terms containing B.

$$\left(x-x_{0}\right)B=ryA-y_{0}A$$

The equation is in standard form.

$$\left(x-x_{0}\right)B=Ary-Ay_{0}$$

Divide both sides by x-x_{0}.

$$\frac{\left(x-x_{0}\right)B}{x-x_{0}}=\frac{A\left(ry-y_{0}\right)}{x-x_{0}}$$

Dividing by x-x_{0} undoes the multiplication by x-x_{0}.

$$B=\frac{A\left(ry-y_{0}\right)}{x-x_{0}}$$