Algebra Examples

$y - 12 = - \frac{7}{12} (x - (- 6))$

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 right side.

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Step 2.1.1

Simplify $- \frac{7}{12} (x - (- 6))$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Multiply $- 1$ by $- 6$ .

$y - 12 = - \frac{7}{12} (x + 6)$

Step 2.1.1.1.2

Apply the distributive property.

$y - 12 = - \frac{7}{12} x - \frac{7}{12} \cdot 6$

Step 2.1.1.1.3

Combine $x$ and $\frac{7}{12}$ .

$y - 12 = - \frac{x \cdot 7}{12} - \frac{7}{12} \cdot 6$

Step 2.1.1.1.4

Cancel the common factor of $6$ .

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Step 2.1.1.1.4.1

Move the leading negative in $- \frac{7}{12}$ into the numerator.

$y - 12 = - \frac{x \cdot 7}{12} + \frac{- 7}{12} \cdot 6$

Step 2.1.1.1.4.2

Factor $6$ out of $12$ .

$y - 12 = - \frac{x \cdot 7}{12} + \frac{- 7}{6 (2)} \cdot 6$

Step 2.1.1.1.4.3

Cancel the common factor.

$y - 12 = - \frac{x \cdot 7}{12} + \frac{- 7}{6 \cdot 2} \cdot 6$

Step 2.1.1.1.4.4

Rewrite the expression.

$y - 12 = - \frac{x \cdot 7}{12} + \frac{- 7}{2}$

Step 2.1.1.2

Simplify each term.

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Step 2.1.1.2.1

Move $7$ to the left of $x$ .

$y - 12 = - \frac{7 \cdot x}{12} + \frac{- 7}{2}$

Step 2.1.1.2.2

Move the negative in front of the fraction.

$y - 12 = - \frac{7 x}{12} - \frac{7}{2}$

Step 2.2

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

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Step 2.2.1

Add $12$ to both sides of the equation.

$y = - \frac{7 x}{12} - \frac{7}{2} + 12$

Step 2.2.2

To write $12$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{7 x}{12} - \frac{7}{2} + 12 \cdot \frac{2}{2}$

Step 2.2.3

Combine $12$ and $\frac{2}{2}$ .

$y = - \frac{7 x}{12} - \frac{7}{2} + \frac{12 \cdot 2}{2}$

Step 2.2.4

Combine the numerators over the common denominator.

$y = - \frac{7 x}{12} + \frac{- 7 + 12 \cdot 2}{2}$

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Multiply $12$ by $2$ .

$y = - \frac{7 x}{12} + \frac{- 7 + 24}{2}$

Step 2.2.5.2

Add $- 7$ and $24$ .

$y = - \frac{7 x}{12} + \frac{17}{2}$

Step 2.3

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

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Step 2.3.1

Reorder terms.

$y = - (\frac{7}{12} x) + \frac{17}{2}$

Step 2.3.2

Remove parentheses.

$y = - \frac{7}{12} x + \frac{17}{2}$