# How do you identify the slope for 3y= x -1/2?

Apr 7, 2015

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

The general linear equation is $y = m x + c$.
$m = s l o p e$
$c$=y-intercept

To find a slope of the line from the liner equation, you have to make sure that all values are in order of the general equation of $y = m x + c$

In $3 y = x - \frac{1}{2}$, all values are in the correct position already. However, we have to simplify this linear equation further to ensure that our linear equation is $y = m x + c$

$3 y$ of $3 y = x - \frac{1}{2}$ has to become $y$ of $y = m x + c$
We can do that by dividing $3 y = x - \frac{1}{2}$ by $3$.

$\frac{3 y}{3} = \frac{x - \frac{1}{2}}{3}$
$y = \frac{1}{3} x - \frac{1}{6}$ as we compare this to the general equation of $y = m x + c$, $m$ which is the slope is multiplied together with $x$, hence, the slope for $3 y = x - \frac{1}{2}$ or $y = \frac{1}{3} x - \frac{1}{6}$ is $\frac{1}{3}$