Solve for y₁ m=(y_2-y_1)/(x_2-x_1)

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

Step 1

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

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

Step 2

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

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

Step 3

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.

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

Step 4

Solve for $y_{1}$ .

Subtract $y_{2}$ from both sides of the equation.

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

Divide each term in $- y_{1} = m x_{2} - m x_{1} - y_{2}$ by $- 1$ and simplify.

Divide each term in $- y_{1} = m x_{2} - m x_{1} - y_{2}$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

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

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

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{m x_{2}}{- 1}$ .

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

Rewrite $- 1 \cdot (m x_{2})$ as $- (m x_{2})$ .

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

Dividing two negative values results in a positive value.

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

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

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

Dividing two negative values results in a positive value.

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

Divide $y_{2}$ by $1$ .

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

Solve for y₁ m=(y_2-y_1)/(x_2-x_1)

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