text: 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 $\frac{1}{3}$
explanation: The document contains a math question and a detailed answer explaining how to identify the slope of the given linear equation.
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distilabel_metadata.role: system
distilabel_metadata.content: 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 $\frac{1}{3}$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a detailed answer explaining how to identify the slope of the given linear equation. 
  
  Label: question-and-answer