Precalculus Examples

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

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 right side.

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Step 2.1.1

Simplify $- 1 (x + \frac{1}{2})$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Rewrite negatives.

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Step 2.1.1.2.1

Rewrite $- 1 x$ as $- x$ .

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

Step 2.1.1.2.2

Rewrite $- 1 (\frac{1}{2})$ as $- (\frac{1}{2})$ .

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

Step 2.2

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

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Step 2.2.1

Subtract $2$ from both sides of the equation.

$y = - x - \frac{1}{2} - 2$

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.2.4

Combine the numerators over the common denominator.

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

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Multiply $- 2$ by $2$ .

$y = - x + \frac{- 1 - 4}{2}$

Step 2.2.5.2

Subtract $4$ from $- 1$ .

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

Step 2.2.6

Move the negative in front of the fraction.

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