Algebra Examples

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

Step 1

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

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Rewrite using the commutative property of multiplication.

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

Step 2

Subtract $y$ from both sides of the equation.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

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

Step 3.2.2

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

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

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

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

Step 3.3.1.2

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

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

Step 3.3.1.3

Dividing two negative values results in a positive value.

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

Step 3.3.1.4

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

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

Step 3.3.1.5

Dividing two negative values results in a positive value.

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

Step 3.3.1.6

Divide $y$ by $1$ .

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