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

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

Solve for m (complex solution)

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&x=x_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine y and -y to get 0.

$$0=m\left(x-x_{1}\right)$$

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

$$0=mx-mx_{1}$$

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

$$mx-mx_{1}=0$$

Combine all terms containing m.

$$\left(x-x_{1}\right)m=0$$

Divide 0 by x-x_{1}.

$$m=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=x_{1}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine y and -y to get 0.

$$0=m\left(x-x_{1}\right)$$

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

$$0=mx-mx_{1}$$

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

$$mx-mx_{1}=0$$

Add mx_{1} to both sides. Anything plus zero gives itself.

$$mx=mx_{1}$$

Divide both sides by m.

$$\frac{mx}{m}=\frac{mx_{1}}{m}$$

Dividing by m undoes the multiplication by m.

$$x=\frac{mx_{1}}{m}$$

Divide mx_{1} by m.

$$x=x_{1}$$

Solve for m

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }&x=x_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine y and -y to get 0.

$$0=m\left(x-x_{1}\right)$$

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

$$0=mx-mx_{1}$$

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

$$mx-mx_{1}=0$$

Combine all terms containing m.

$$\left(x-x_{1}\right)m=0$$

Divide 0 by x-x_{1}.

$$m=0$$

Solve for x

$$\left\{\begin{matrix}\\x=x_{1}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine y and -y to get 0.

$$0=m\left(x-x_{1}\right)$$

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

$$0=mx-mx_{1}$$

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

$$mx-mx_{1}=0$$

Add mx_{1} to both sides. Anything plus zero gives itself.

$$mx=mx_{1}$$

Divide both sides by m.

$$\frac{mx}{m}=\frac{mx_{1}}{m}$$

Dividing by m undoes the multiplication by m.

$$x=\frac{mx_{1}}{m}$$

Divide mx_{1} by m.

$$x=x_{1}$$