Algebra Examples

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

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

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Step 2.1.1.1

Simplify each term.

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Step 2.1.1.1.1

Apply the distributive property.

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

Step 2.1.1.1.2

Multiply $2$ by $- 1$ .

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

Step 2.1.1.2

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.1.1.3

Simplify terms.

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Step 2.1.1.3.1

Combine $2 y$ and $\frac{3}{3}$ .

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

Step 2.1.1.3.2

Combine the numerators over the common denominator.

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

Step 2.1.1.4

Multiply $3$ by $2$ .

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

Step 2.1.1.5

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.1.1.6

Simplify terms.

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Step 2.1.1.6.1

Combine $- 2$ and $\frac{3}{3}$ .

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

Step 2.1.1.6.2

Combine the numerators over the common denominator.

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

Step 2.1.1.7

Simplify the numerator.

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Step 2.1.1.7.1

Multiply $- 2$ by $3$ .

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

Step 2.1.1.7.2

Subtract $6$ from $5$ .

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

Step 2.2

Multiply both sides by $3$ .

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

Step 2.3

Simplify.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Simplify $\frac{6 y + 6 x - 1}{3} \cdot 3$ .

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Step 2.3.1.1.1

Cancel the common factor of $3$ .

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Step 2.3.1.1.1.1

Cancel the common factor.

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

Step 2.3.1.1.1.2

Rewrite the expression.

$6 y + 6 x - 1 = - 2 \cdot 3$

Step 2.3.1.1.2

Reorder $6 y$ and $6 x$ .

$6 x + 6 y - 1 = - 2 \cdot 3$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Multiply $- 2$ by $3$ .

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

Step 2.4

Solve for $y$ .

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Step 2.4.1

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

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Step 2.4.1.1

Subtract $6 x$ from both sides of the equation.

$6 y - 1 = - 6 - 6 x$

Step 2.4.1.2

Add $1$ to both sides of the equation.

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

Step 2.4.1.3

Add $- 6$ and $1$ .

$6 y = - 6 x - 5$

Step 2.4.2

Divide each term in $6 y = - 6 x - 5$ by $6$ and simplify.

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Step 2.4.2.1

Divide each term in $6 y = - 6 x - 5$ by $6$ .

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

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Cancel the common factor of $6$ .

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Step 2.4.2.2.1.1

Cancel the common factor.

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

Step 2.4.2.2.1.2

Divide $y$ by $1$ .

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

Step 2.4.2.3

Simplify the right side.

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Step 2.4.2.3.1

Simplify each term.

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Step 2.4.2.3.1.1

Cancel the common factor of $- 6$ and $6$ .

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Step 2.4.2.3.1.1.1

Factor $6$ out of $- 6 x$ .

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

Step 2.4.2.3.1.1.2

Cancel the common factors.

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Step 2.4.2.3.1.1.2.1

Factor $6$ out of $6$ .

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

Step 2.4.2.3.1.1.2.2

Cancel the common factor.

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

Step 2.4.2.3.1.1.2.3

Rewrite the expression.

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

Step 2.4.2.3.1.1.2.4

Divide $- x$ by $1$ .

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

Step 2.4.2.3.1.2

Move the negative in front of the fraction.

$y = - x - \frac{5}{6}$