Algebra Examples

$x - \frac{1}{2} (y - 6) = 8$

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

Apply the distributive property.

$x - \frac{1}{2} y - \frac{1}{2} \cdot - 6 = 8$

Step 2.1.1.2

Combine $y$ and $\frac{1}{2}$ .

$x - \frac{y}{2} - \frac{1}{2} \cdot - 6 = 8$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x - \frac{y}{2} + \frac{- 1}{2} \cdot - 6 = 8$

Step 2.1.1.3.2

Factor $2$ out of $- 6$ .

$x - \frac{y}{2} + \frac{- 1}{2} \cdot (2 (- 3)) = 8$

Step 2.1.1.3.3

Cancel the common factor.

$x - \frac{y}{2} + \frac{- 1}{2} \cdot (2 \cdot - 3) = 8$

Step 2.1.1.3.4

Rewrite the expression.

$x - \frac{y}{2} - 1 \cdot - 3 = 8$

Step 2.1.1.4

Multiply $- 1$ by $- 3$ .

$x - \frac{y}{2} + 3 = 8$

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 $x$ from both sides of the equation.

$- \frac{y}{2} + 3 = 8 - x$

Step 2.2.2

Subtract $3$ from both sides of the equation.

$- \frac{y}{2} = 8 - x - 3$

Step 2.2.3

Subtract $3$ from $8$ .

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

Step 2.3

Multiply both sides of the equation by $- 2$ .

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

Step 2.4

Simplify both sides of the equation.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Simplify $- 2 (- \frac{y}{2})$ .

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Step 2.4.1.1.1

Cancel the common factor of $2$ .

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Step 2.4.1.1.1.1

Move the leading negative in $- \frac{y}{2}$ into the numerator.

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

Step 2.4.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 2.4.1.1.1.3

Cancel the common factor.

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

Step 2.4.1.1.1.4

Rewrite the expression.

$- - y = - 2 (- x + 5)$

Step 2.4.1.1.2

Multiply.

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Step 2.4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 2 (- x + 5)$

Step 2.4.1.1.2.2

Multiply $y$ by $1$ .

$y = - 2 (- x + 5)$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Simplify $- 2 (- x + 5)$ .

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Step 2.4.2.1.1

Apply the distributive property.

$y = - 2 (- x) - 2 \cdot 5$

Step 2.4.2.1.2

Multiply.

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Step 2.4.2.1.2.1

Multiply $- 1$ by $- 2$ .

$y = 2 x - 2 \cdot 5$

Step 2.4.2.1.2.2

Multiply $- 2$ by $5$ .

$y = 2 x - 10$