Algebra Examples

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

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.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

Cancel the common factor.

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

Step 3.1.1.2

Rewrite the expression.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

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

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Step 3.2.1.1

Apply the distributive property.

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

Step 3.2.1.2

Rewrite using the commutative property of multiplication.

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

Step 4

Solve for $y_{1}$ .

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Step 4.1

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

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

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

Step 4.2.2.2

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

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

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Simplify each term.

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Step 4.2.3.1.1

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

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

Step 4.2.3.1.2

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

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

Step 4.2.3.1.3

Dividing two negative values results in a positive value.

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

Step 4.2.3.1.4

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

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

Step 4.2.3.1.5

Dividing two negative values results in a positive value.

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

Step 4.2.3.1.6

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

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