Algebra Examples

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

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 $\frac{3 - 2}{- 1 - 3} (x - 2)$ .

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Step 2.1.1.1

Simplify the expression.

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Step 2.1.1.1.1

Subtract $2$ from $3$ .

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

Step 2.1.1.1.2

Subtract $3$ from $- 1$ .

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

Step 2.1.1.1.3

Move the negative in front of the fraction.

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

Step 2.1.1.2

Apply the distributive property.

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

Step 2.1.1.3

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

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

Step 2.1.1.4

Cancel the common factor of $2$ .

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Step 2.1.1.4.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Step 2.1.1.4.2

Factor $2$ out of $4$ .

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

Step 2.1.1.4.3

Factor $2$ out of $- 2$ .

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

Step 2.1.1.4.4

Cancel the common factor.

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

Step 2.1.1.4.5

Rewrite the expression.

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

Step 2.1.1.5

Combine $\frac{- 1}{2}$ and $- 1$ .

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

Step 2.1.1.6

Multiply $- 1$ by $- 1$ .

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

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 $1$ from both sides of the equation.

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

Step 2.2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.2.3

Combine $- 1$ and $\frac{2}{2}$ .

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

Step 2.2.4

Combine the numerators over the common denominator.

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

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Multiply $- 1$ by $2$ .

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

Step 2.2.5.2

Subtract $2$ from $1$ .

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

Step 2.2.6

Move the negative in front of the fraction.

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

Step 2.3

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

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Step 2.3.1

Reorder terms.

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

Step 2.3.2

Remove parentheses.

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