Solve for y₂ m=(y_2-y_1)/(x_2-x_1)

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

Rewrite the equation as $\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = m$ .

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

Multiply both sides by $x_{2} - x_{1}$ .

$\frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x_{2} - x_{1}) = m (x_{2} - x_{1})$

Simplify.

Simplify the left side.

Cancel the common factor of $x_{2} - x_{1}$ .

Cancel the common factor.

$\frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x_{2} - x_{1}) = m (x_{2} - x_{1})$

Rewrite the expression.

$y_{2} - y_{1} = m (x_{2} - x_{1})$

Simplify the right side.

Simplify $m (x_{2} - x_{1})$ .

Apply the distributive property.

$y_{2} - y_{1} = m x_{2} + m (- x_{1})$

Rewrite using the commutative property of multiplication.

$y_{2} - y_{1} = m x_{2} - m x_{1}$

Add $y_{1}$ to both sides of the equation.

$y_{2} = m x_{2} - m x_{1} + y_{1}$