Solve for y₁ y-y_1=m(x-x_1)

$y - y_{1} = m (x - x_{1})$

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

Rewrite.

$y - y_{1} = 0 + 0 + m (x - x_{1})$

Simplify by adding zeros.

$y - y_{1} = m (x - x_{1})$

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

$y - y_{1} = m x - m x_{1}$

Subtract $y$ from both sides of the equation.

$- y_{1} = m x - m x_{1} - y$

Divide each term in $- y_{1} = m x - m x_{1} - y$ by $- 1$ and simplify.

Divide each term in $- y_{1} = m x - m x_{1} - y$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y_{1}$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{m x}{- 1}$ .

$y_{1} = - 1 \cdot (m x) + \frac{- m x_{1}}{- 1} + \frac{- y}{- 1}$

Rewrite $- 1 \cdot (m x)$ as $- (m x)$ .

$y_{1} = - (m x) + \frac{- m x_{1}}{- 1} + \frac{- y}{- 1}$

Dividing two negative values results in a positive value.

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

Divide $m x_{1}$ by $1$ .

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

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

$y_{1} = - m x + m x_{1} + y$