Algebra Examples

$1 - \frac{2 y - 7 x}{2} = 7 x + 6$

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 $1 - \frac{2 y - 7 x}{2}$ .

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Step 2.1.1.1

Combine into one fraction.

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Step 2.1.1.1.1

Write $1$ as a fraction with a common denominator.

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

Step 2.1.1.1.2

Combine the numerators over the common denominator.

$\frac{2 - (2 y - 7 x)}{2} = 7 x + 6$

Step 2.1.1.2

Simplify the numerator.

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Step 2.1.1.2.1

Apply the distributive property.

$\frac{2 - (2 y) - (- 7 x)}{2} = 7 x + 6$

Step 2.1.1.2.2

Multiply $2$ by $- 1$ .

$\frac{2 - 2 y - (- 7 x)}{2} = 7 x + 6$

Step 2.1.1.2.3

Multiply $- 7$ by $- 1$ .

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

Step 2.2

Multiply both sides by $2$ .

$\frac{2 - 2 y + 7 x}{2} \cdot 2 = (7 x + 6) \cdot 2$

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

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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.

$\frac{2 - 2 y + 7 x}{2} \cdot 2 = (7 x + 6) \cdot 2$

Step 2.3.1.1.1.2

Rewrite the expression.

$2 - 2 y + 7 x = (7 x + 6) \cdot 2$

Step 2.3.1.1.2

Simplify the expression.

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Step 2.3.1.1.2.1

Move $2$ .

$- 2 y + 7 x + 2 = (7 x + 6) \cdot 2$

Step 2.3.1.1.2.2

Reorder $- 2 y$ and $7 x$ .

$7 x - 2 y + 2 = (7 x + 6) \cdot 2$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $(7 x + 6) \cdot 2$ .

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Step 2.3.2.1.1

Apply the distributive property.

$7 x - 2 y + 2 = 7 x \cdot 2 + 6 \cdot 2$

Step 2.3.2.1.2

Multiply.

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Step 2.3.2.1.2.1

Multiply $2$ by $7$ .

$7 x - 2 y + 2 = 14 x + 6 \cdot 2$

Step 2.3.2.1.2.2

Multiply $6$ by $2$ .

$7 x - 2 y + 2 = 14 x + 12$

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 $7 x$ from both sides of the equation.

$- 2 y + 2 = 14 x + 12 - 7 x$

Step 2.4.1.2

Subtract $2$ from both sides of the equation.

$- 2 y = 14 x + 12 - 7 x - 2$

Step 2.4.1.3

Subtract $7 x$ from $14 x$ .

$- 2 y = 7 x + 12 - 2$

Step 2.4.1.4

Subtract $2$ from $12$ .

$- 2 y = 7 x + 10$

Step 2.4.2

Divide each term in $- 2 y = 7 x + 10$ by $- 2$ and simplify.

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Step 2.4.2.1

Divide each term in $- 2 y = 7 x + 10$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{7 x}{- 2} + \frac{10}{- 2}$

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Cancel the common factor of $- 2$ .

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Step 2.4.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{7 x}{- 2} + \frac{10}{- 2}$

Step 2.4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{7 x}{- 2} + \frac{10}{- 2}$

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

Move the negative in front of the fraction.

$y = - \frac{7 x}{2} + \frac{10}{- 2}$

Step 2.4.2.3.1.2

Divide $10$ by $- 2$ .

$y = - \frac{7 x}{2} - 5$

Step 2.5

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

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Step 2.5.1

Reorder terms.

$y = - (\frac{7}{2} x) - 5$

Step 2.5.2

Remove parentheses.

$y = - \frac{7}{2} x - 5$