Algebra Examples

$6 - \frac{2 y - 2 x}{2} = 3 x + 5$

Step 1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Cancel the common factor of $2 y - 2 x$ and $2$ .

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Step 2.1.1.1.1

Factor $2$ out of $2 y$ .

$6 - \frac{2 (y) - 2 x}{2} = 3 x + 5$

Step 2.1.1.1.2

Factor $2$ out of $- 2 x$ .

$6 - \frac{2 (y) + 2 (- x)}{2} = 3 x + 5$

Step 2.1.1.1.3

Factor $2$ out of $2 (y) + 2 (- x)$ .

$6 - \frac{2 (y - x)}{2} = 3 x + 5$

Step 2.1.1.1.4

Cancel the common factors.

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Step 2.1.1.1.4.1

Factor $2$ out of $2$ .

$6 - \frac{2 (y - x)}{2 (1)} = 3 x + 5$

Step 2.1.1.1.4.2

Cancel the common factor.

$6 - \frac{2 (y - x)}{2 \cdot 1} = 3 x + 5$

Step 2.1.1.1.4.3

Rewrite the expression.

$6 - \frac{y - x}{1} = 3 x + 5$

Step 2.1.1.1.4.4

Divide $y - x$ by $1$ .

$6 - (y - x) = 3 x + 5$

Step 2.1.1.2

Apply the distributive property.

$6 - y - - x = 3 x + 5$

Step 2.1.1.3

Multiply $- - x$ .

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Step 2.1.1.3.1

Multiply $- 1$ by $- 1$ .

$6 - y + 1 x = 3 x + 5$

Step 2.1.1.3.2

Multiply $x$ by $1$ .

$6 - y + x = 3 x + 5$

Step 2.2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.1

Subtract $6$ from both sides of the equation.

$- y + x = 3 x + 5 - 6$

Step 2.2.2

Subtract $x$ from both sides of the equation.

$- y = 3 x + 5 - 6 - x$

Step 2.2.3

Subtract $x$ from $3 x$ .

$- y = 2 x + 5 - 6$

Step 2.2.4

Subtract $6$ from $5$ .

$- y = 2 x - 1$

Step 2.3

Divide each term in $- y = 2 x - 1$ by $- 1$ and simplify.

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Step 2.3.1

Divide each term in $- y = 2 x - 1$ by $- 1$ .

$\frac{- y}{- 1} = \frac{2 x}{- 1} + \frac{- 1}{- 1}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{2 x}{- 1} + \frac{- 1}{- 1}$

Step 2.3.2.2

Divide $y$ by $1$ .

$y = \frac{2 x}{- 1} + \frac{- 1}{- 1}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

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

$y = - 1 \cdot (2 x) + \frac{- 1}{- 1}$

Step 2.3.3.1.2

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

$y = - (2 x) + \frac{- 1}{- 1}$

Step 2.3.3.1.3

Multiply $2$ by $- 1$ .

$y = - 2 x + \frac{- 1}{- 1}$

Step 2.3.3.1.4

Divide $- 1$ by $- 1$ .

$y = - 2 x + 1$