Solve frac{y_{2}-y_{1}}{x_{2}-x_{1}}=k

$$\frac { y _ { 2 } - y _ { 1 } } { x _ { 2 } - x _ { 1 } } = k$$

Solve for k

$$k=-\frac{y_{2}-y_{1}}{x_{1}-x_{2}}$$

$$x_{2}\neq x_{1}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -x_{1}+x_{2}.

$$y_{2}-y_{1}=k\left(-x_{1}+x_{2}\right)$$

Use the distributive property to multiply k by -x_{1}+x_{2}.

$$y_{2}-y_{1}=-kx_{1}+kx_{2}$$

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

$$-kx_{1}+kx_{2}=y_{2}-y_{1}$$

Combine all terms containing k.

$$\left(-x_{1}+x_{2}\right)k=y_{2}-y_{1}$$

The equation is in standard form.

$$\left(x_{2}-x_{1}\right)k=y_{2}-y_{1}$$

Divide both sides by x_{2}-x_{1}.

$$\frac{\left(x_{2}-x_{1}\right)k}{x_{2}-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$

Dividing by x_{2}-x_{1} undoes the multiplication by x_{2}-x_{1}.

$$k=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$

Solve for x_1

$$\left\{\begin{matrix}x_{1}=\frac{kx_{2}+y_{1}-y_{2}}{k}\text{, }&y_{2}\neq y_{1}\text{ and }k\neq 0\\x_{1}\neq x_{2}\text{, }&k=0\text{ and }y_{2}=y_{1}\end{matrix}\right.$$