Precalculus Examples

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

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

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Step 1.2.1.1

Apply the distributive property.

$y - 3 = - \frac{1}{2} x - \frac{1}{2} \cdot - 2$

Step 1.2.1.2

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

$y - 3 = - \frac{x}{2} - \frac{1}{2} \cdot - 2$

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.

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

Step 1.2.1.3.2

Factor $2$ out of $- 2$ .

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

Step 1.2.1.3.3

Cancel the common factor.

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

Step 1.2.1.3.4

Rewrite the expression.

$y - 3 = - \frac{x}{2} - 1 \cdot - 1$

Step 1.2.1.4

Multiply $- 1$ by $- 1$ .

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

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 $3$ to both sides of the equation.

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

Step 1.3.2

Add $1$ and $3$ .

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

Step 1.4

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

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Step 1.4.1

Reorder terms.

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

Step 1.4.2

Remove parentheses.

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

Step 2

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

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

Step 3