Pre-Algebra Examples

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

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Simplify the right side.

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Step 1.2.1

Simplify $- \frac{1}{2} \cdot (x + 4)$ .

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Step 1.2.1.1

Apply the distributive property.

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

Step 1.2.1.2

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

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

Step 1.2.1.3

Cancel the common factor of $2$ .

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Step 1.2.1.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 1.2.1.3.2

Factor $2$ out of $4$ .

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

Step 1.2.1.3.3

Cancel the common factor.

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

Step 1.2.1.3.4

Rewrite the expression.

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

Step 1.2.1.4

Multiply $- 1$ by $2$ .

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

Step 1.3

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

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Step 1.3.1

Add $2$ to both sides of the equation.

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

Step 1.3.2

Combine the opposite terms in $- \frac{x}{2} - 2 + 2$ .

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Step 1.3.2.1

Add $- 2$ and $2$ .

$y = - \frac{x}{2} + 0$

Step 1.3.2.2

Add $- \frac{x}{2}$ and $0$ .

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

Step 1.4

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

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Step 1.4.1

Reorder terms.

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

Step 1.4.2

Remove parentheses.

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

Step 2

Using the slope-intercept form, the slope is $- \frac{1}{2}$ .

$m = - \frac{1}{2}$

Step 3