Solve y-y_{1}=m(x-3/4)

$$y - y _ { 1 } = m ( x - \frac { 3 } { 4 } )$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{4\left(y-y_{1}\right)}{3-4x}\text{, }&x\neq \frac{3}{4}\\m\in \mathrm{C}\text{, }&y=y_{1}\text{ and }x=\frac{3}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x-\frac{3}{4}.

$$y-y_{1}=mx-\frac{3}{4}m$$

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

$$mx-\frac{3}{4}m=y-y_{1}$$

Combine all terms containing m.

$$\left(x-\frac{3}{4}\right)m=y-y_{1}$$

Divide both sides by x-\frac{3}{4}.

$$\frac{\left(x-\frac{3}{4}\right)m}{x-\frac{3}{4}}=\frac{y-y_{1}}{x-\frac{3}{4}}$$

Dividing by x-\frac{3}{4} undoes the multiplication by x-\frac{3}{4}.

$$m=\frac{y-y_{1}}{x-\frac{3}{4}}$$

Divide y-y_{1} by x-\frac{3}{4}.

$$m=\frac{4\left(y-y_{1}\right)}{4x-3}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y}{m}-\frac{y_{1}}{m}+\frac{3}{4}\text{, }&m\neq 0\\x\in \mathrm{C}\text{, }&y=y_{1}\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x-\frac{3}{4}.

$$y-y_{1}=mx-\frac{3}{4}m$$

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

$$mx-\frac{3}{4}m=y-y_{1}$$

Add \frac{3}{4}m to both sides.

$$mx=y-y_{1}+\frac{3}{4}m$$

The equation is in standard form.

$$mx=\frac{3m}{4}+y-y_{1}$$

Divide both sides by m.

$$\frac{mx}{m}=\frac{\frac{3m}{4}+y-y_{1}}{m}$$

Dividing by m undoes the multiplication by m.

$$x=\frac{\frac{3m}{4}+y-y_{1}}{m}$$

Divide y-y_{1}+\frac{3m}{4} by m.

$$x=\frac{y-y_{1}}{m}+\frac{3}{4}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{4\left(y-y_{1}\right)}{3-4x}\text{, }&x\neq \frac{3}{4}\\m\in \mathrm{R}\text{, }&y=y_{1}\text{ and }x=\frac{3}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x-\frac{3}{4}.

$$y-y_{1}=mx-\frac{3}{4}m$$

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

$$mx-\frac{3}{4}m=y-y_{1}$$

Combine all terms containing m.

$$\left(x-\frac{3}{4}\right)m=y-y_{1}$$

Divide both sides by x-\frac{3}{4}.

$$\frac{\left(x-\frac{3}{4}\right)m}{x-\frac{3}{4}}=\frac{y-y_{1}}{x-\frac{3}{4}}$$

Dividing by x-\frac{3}{4} undoes the multiplication by x-\frac{3}{4}.

$$m=\frac{y-y_{1}}{x-\frac{3}{4}}$$

Divide y-y_{1} by x-\frac{3}{4}.

$$m=\frac{4\left(y-y_{1}\right)}{4x-3}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{y}{m}-\frac{y_{1}}{m}+\frac{3}{4}\text{, }&m\neq 0\\x\in \mathrm{R}\text{, }&y=y_{1}\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply m by x-\frac{3}{4}.

$$y-y_{1}=mx-\frac{3}{4}m$$

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

$$mx-\frac{3}{4}m=y-y_{1}$$

Add \frac{3}{4}m to both sides.

$$mx=y-y_{1}+\frac{3}{4}m$$

The equation is in standard form.

$$mx=\frac{3m}{4}+y-y_{1}$$

Divide both sides by m.

$$\frac{mx}{m}=\frac{\frac{3m}{4}+y-y_{1}}{m}$$

Dividing by m undoes the multiplication by m.

$$x=\frac{\frac{3m}{4}+y-y_{1}}{m}$$

Divide y-y_{1}+\frac{3m}{4} by m.

$$x=\frac{y-y_{1}}{m}+\frac{3}{4}$$