How do you find the slope given 3y= x -1/2?

Sep 6, 2017

See a solution process below:

Explanation:

First, we can put the equation into slope-intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

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

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

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} y}{\cancel{\textcolor{red}{3}}} = \frac{x}{\textcolor{red}{3}} - \frac{\frac{1}{2}}{\textcolor{red}{3}}$

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

$y = \textcolor{red}{\frac{1}{3}} x - \textcolor{b l u e}{\frac{1}{6}}$

Therefore, the slope of the line represented by this equation is:

$\textcolor{red}{m = \frac{1}{3}}$