Write in Slope-Intercept Form y-2=-1/2(x-1)

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

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.

Simplify the right side.

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

Apply the distributive property.

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

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

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

Multiply $- \frac{1}{2} \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{1}{2}$ by $1$ .

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

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

Add $2$ to both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

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

Add $1$ and $4$ .

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

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

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{5}{2}$

Remove parentheses.

$y = - \frac{1}{2} x + \frac{5}{2}$