Precalculus Examples

$y + 4 = - \frac{1}{4} \cdot (x + 1)$

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 $- \frac{1}{4} \cdot (x + 1)$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Combine $x$ and $\frac{1}{4}$ .

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

Step 2.1.1.3

Multiply $- 1$ by $1$ .

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

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 $4$ from both sides of the equation.

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

Step 2.2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{x}{4} - \frac{1}{4} - 4 \cdot \frac{4}{4}$

Step 2.2.3

Combine $- 4$ and $\frac{4}{4}$ .

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

Step 2.2.4

Combine the numerators over the common denominator.

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

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Multiply $- 4$ by $4$ .

$y = - \frac{x}{4} + \frac{- 1 - 16}{4}$

Step 2.2.5.2

Subtract $16$ from $- 1$ .

$y = - \frac{x}{4} + \frac{- 17}{4}$

Step 2.2.6

Move the negative in front of the fraction.

$y = - \frac{x}{4} - \frac{17}{4}$

Step 2.3

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

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Step 2.3.1

Reorder terms.

$y = - (\frac{1}{4} x) - \frac{17}{4}$

Step 2.3.2

Remove parentheses.

$y = - \frac{1}{4} x - \frac{17}{4}$