Solve (y-y_{1})=m(x-x_{1})

$$( y - y _ { 1 } ) = m ( x - x _ { 1 } )$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{y-y_{1}}{x-x_{1}}\text{, }&x\neq x_{1}\\m\in \mathrm{C}\text{, }&y=y_{1}\text{ and }x=x_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x-x_{1}.

$$y-y_{1}=mx-mx_{1}$$

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

$$mx-mx_{1}=y-y_{1}$$

Combine all terms containing m.

$$\left(x-x_{1}\right)m=y-y_{1}$$

Divide both sides by x-x_{1}.

$$\frac{\left(x-x_{1}\right)m}{x-x_{1}}=\frac{y-y_{1}}{x-x_{1}}$$

Dividing by x-x_{1} undoes the multiplication by x-x_{1}.

$$m=\frac{y-y_{1}}{x-x_{1}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{mx_{1}+y-y_{1}}{m}\text{, }&m\neq 0\\x\in \mathrm{C}\text{, }&y=y_{1}\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x-x_{1}.

$$y-y_{1}=mx-mx_{1}$$

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

$$mx-mx_{1}=y-y_{1}$$

Add mx_{1} to both sides.

$$mx=y-y_{1}+mx_{1}$$

The equation is in standard form.

$$mx=mx_{1}+y-y_{1}$$

Divide both sides by m.

$$\frac{mx}{m}=\frac{mx_{1}+y-y_{1}}{m}$$

Dividing by m undoes the multiplication by m.

$$x=\frac{mx_{1}+y-y_{1}}{m}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{y-y_{1}}{x-x_{1}}\text{, }&x\neq x_{1}\\m\in \mathrm{R}\text{, }&y=y_{1}\text{ and }x=x_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x-x_{1}.

$$y-y_{1}=mx-mx_{1}$$

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

$$mx-mx_{1}=y-y_{1}$$

Combine all terms containing m.

$$\left(x-x_{1}\right)m=y-y_{1}$$

Divide both sides by x-x_{1}.

$$\frac{\left(x-x_{1}\right)m}{x-x_{1}}=\frac{y-y_{1}}{x-x_{1}}$$

Dividing by x-x_{1} undoes the multiplication by x-x_{1}.

$$m=\frac{y-y_{1}}{x-x_{1}}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{mx_{1}+y-y_{1}}{m}\text{, }&m\neq 0\\x\in \mathrm{R}\text{, }&y=y_{1}\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x-x_{1}.

$$y-y_{1}=mx-mx_{1}$$

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

$$mx-mx_{1}=y-y_{1}$$

Add mx_{1} to both sides.

$$mx=y-y_{1}+mx_{1}$$

The equation is in standard form.

$$mx=mx_{1}+y-y_{1}$$

Divide both sides by m.

$$\frac{mx}{m}=\frac{mx_{1}+y-y_{1}}{m}$$

Dividing by m undoes the multiplication by m.

$$x=\frac{mx_{1}+y-y_{1}}{m}$$