Write in Slope-Intercept Form y+5/3=1/2(x-2)

$y + \frac{5}{3} = \frac{1}{2} (x - 2)$

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.

Simplify the right side.

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

Apply the distributive property.

$y + \frac{5}{3} = \frac{1}{2} x + \frac{1}{2} \cdot - 2$

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

$y + \frac{5}{3} = \frac{x}{2} + \frac{1}{2} \cdot - 2$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$y + \frac{5}{3} = \frac{x}{2} + \frac{1}{2} \cdot (2 (- 1))$

Cancel the common factor.

$y + \frac{5}{3} = \frac{x}{2} + \frac{1}{2} \cdot (2 \cdot - 1)$

Rewrite the expression.

$y + \frac{5}{3} = \frac{x}{2} - 1$

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

Subtract $\frac{5}{3}$ from both sides of the equation.

$y = \frac{x}{2} - 1 - \frac{5}{3}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{x}{2} - 1 \cdot \frac{3}{3} - \frac{5}{3}$

Combine $- 1$ and $\frac{3}{3}$ .

$y = \frac{x}{2} + \frac{- 1 \cdot 3}{3} - \frac{5}{3}$

Combine the numerators over the common denominator.

$y = \frac{x}{2} + \frac{- 1 \cdot 3 - 5}{3}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$y = \frac{x}{2} + \frac{- 3 - 5}{3}$

Subtract $5$ from $- 3$ .

$y = \frac{x}{2} + \frac{- 8}{3}$

Move the negative in front of the fraction.

$y = \frac{x}{2} - \frac{8}{3}$

Reorder terms.

$y = \frac{1}{2} x - \frac{8}{3}$