# Solve for y in y + 1/2 = -1/3(x+1/2)?

Apr 7, 2015

The solution is $y = - \frac{1}{3} x - \frac{2}{3}$.

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

Perform the distributive property first.

$y + \frac{1}{2} = - \frac{1}{3} x - \frac{1}{6}$

Subtract $\frac{1}{2}$ from both sides. The common denominator for $\frac{1}{2}$

and $\frac{1}{6}$ is $6$. So $\frac{1}{2} \cdot \frac{3}{3} = \frac{3}{6}$.

$y = - \frac{1}{3} x - \frac{1}{6} - \frac{3}{6}$ =

$y = \frac{1}{3} x - \frac{4}{6}$ =

Reduce $\frac{4}{6}$ to $\frac{2}{3}$.

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

If this is supposed to be the slope-intercept equation for a line, the slope is $- \frac{1}{3}$ and the y-intercept is $- \frac{2}{3}$.