Algebra Examples

$\frac{6 x + 2}{4} - 7 y = 2 - 8 y$

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 $\frac{6 x + 2}{4} - 7 y$ .

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Step 2.1.1.1

Cancel the common factor of $6 x + 2$ and $4$ .

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Step 2.1.1.1.1

Factor $2$ out of $6 x$ .

$\frac{2 (3 x) + 2}{4} - 7 y = 2 - 8 y$

Step 2.1.1.1.2

Factor $2$ out of $2$ .

$\frac{2 (3 x) + 2 (1)}{4} - 7 y = 2 - 8 y$

Step 2.1.1.1.3

Factor $2$ out of $2 (3 x) + 2 (1)$ .

$\frac{2 (3 x + 1)}{4} - 7 y = 2 - 8 y$

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 $4$ .

$\frac{2 (3 x + 1)}{2 (2)} - 7 y = 2 - 8 y$

Step 2.1.1.1.4.2

Cancel the common factor.

$\frac{2 (3 x + 1)}{2 \cdot 2} - 7 y = 2 - 8 y$

Step 2.1.1.1.4.3

Rewrite the expression.

$\frac{3 x + 1}{2} - 7 y = 2 - 8 y$

Step 2.1.1.2

To write $- 7 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x + 1}{2} - 7 y \cdot \frac{2}{2} = 2 - 8 y$

Step 2.1.1.3

Combine $- 7 y$ and $\frac{2}{2}$ .

$\frac{3 x + 1}{2} + \frac{- 7 y \cdot 2}{2} = 2 - 8 y$

Step 2.1.1.4

Combine the numerators over the common denominator.

$\frac{3 x + 1 - 7 y \cdot 2}{2} = 2 - 8 y$

Step 2.1.1.5

Multiply $2$ by $- 7$ .

$\frac{3 x + 1 - 14 y}{2} = 2 - 8 y$

Step 2.2

Multiply both sides by $2$ .

$\frac{3 x + 1 - 14 y}{2} \cdot 2 = (2 - 8 y) \cdot 2$

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 $\frac{3 x + 1 - 14 y}{2} \cdot 2$ .

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Step 2.3.1.1.1

Cancel the common factor of $2$ .

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Step 2.3.1.1.1.1

Cancel the common factor.

$\frac{3 x + 1 - 14 y}{2} \cdot 2 = (2 - 8 y) \cdot 2$

Step 2.3.1.1.1.2

Rewrite the expression.

$3 x + 1 - 14 y = (2 - 8 y) \cdot 2$

Step 2.3.1.1.2

Move $1$ .

$3 x - 14 y + 1 = (2 - 8 y) \cdot 2$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $(2 - 8 y) \cdot 2$ .

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Step 2.3.2.1.1

Apply the distributive property.

$3 x - 14 y + 1 = 2 \cdot 2 - 8 y \cdot 2$

Step 2.3.2.1.2

Simplify the expression.

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Step 2.3.2.1.2.1

Multiply $2$ by $2$ .

$3 x - 14 y + 1 = 4 - 8 y \cdot 2$

Step 2.3.2.1.2.2

Multiply $2$ by $- 8$ .

$3 x - 14 y + 1 = 4 - 16 y$

Step 2.3.2.1.2.3

Reorder $4$ and $- 16 y$ .

$3 x - 14 y + 1 = - 16 y + 4$

Step 2.4

Solve for $y$ .

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Step 2.4.1

Move all terms containing $y$ to the left side of the equation.

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Step 2.4.1.1

Add $16 y$ to both sides of the equation.

$3 x - 14 y + 1 + 16 y = 4$

Step 2.4.1.2

Add $- 14 y$ and $16 y$ .

$3 x + 2 y + 1 = 4$

Step 2.4.2

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

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Step 2.4.2.1

Subtract $3 x$ from both sides of the equation.

$2 y + 1 = 4 - 3 x$

Step 2.4.2.2

Subtract $1$ from both sides of the equation.

$2 y = 4 - 3 x - 1$

Step 2.4.2.3

Subtract $1$ from $4$ .

$2 y = - 3 x + 3$

Step 2.4.3

Divide each term in $2 y = - 3 x + 3$ by $2$ and simplify.

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Step 2.4.3.1

Divide each term in $2 y = - 3 x + 3$ by $2$ .

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

Step 2.4.3.2

Simplify the left side.

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Step 2.4.3.2.1

Cancel the common factor of $2$ .

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Step 2.4.3.2.1.1

Cancel the common factor.

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

Step 2.4.3.2.1.2

Divide $y$ by $1$ .

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

Step 2.4.3.3

Simplify the right side.

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Step 2.4.3.3.1

Move the negative in front of the fraction.

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

Step 2.5

Write in $y = m x + b$ form.

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Step 2.5.1

Reorder terms.

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

Step 2.5.2

Remove parentheses.

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