Solve y=kx-k+4

$$y = k x - k + 4$$

Solve for k (complex solution)

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

Steps for Solving Linear Equation

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

$$kx-k+4=y$$

Subtract 4 from both sides.

$$kx-k=y-4$$

Combine all terms containing k.

$$\left(x-1\right)k=y-4$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)k}{x-1}=\frac{y-4}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$k=\frac{y-4}{x-1}$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

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

$$kx-k+4=y$$

Add k to both sides.

$$kx+4=y+k$$

Subtract 4 from both sides.

$$kx=y+k-4$$

Divide both sides by k.

$$\frac{kx}{k}=\frac{y+k-4}{k}$$

Dividing by k undoes the multiplication by k.

$$x=\frac{y+k-4}{k}$$

Solve for k

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

Steps for Solving Linear Equation

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

$$kx-k+4=y$$

Subtract 4 from both sides.

$$kx-k=y-4$$

Combine all terms containing k.

$$\left(x-1\right)k=y-4$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)k}{x-1}=\frac{y-4}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$k=\frac{y-4}{x-1}$$

Solve for x

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

Steps for Solving Linear Equation

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

$$kx-k+4=y$$

Add k to both sides.

$$kx+4=y+k$$

Subtract 4 from both sides.

$$kx=y+k-4$$

Divide both sides by k.

$$\frac{kx}{k}=\frac{y+k-4}{k}$$

Dividing by k undoes the multiplication by k.

$$x=\frac{y+k-4}{k}$$