Since you want to get to slope-intercept form, [tex] y=mx+b [/tex], you want to get y isolated on one side of the equation.
We are given:
[tex] 3y-x=6 [/tex]
Let us first get 3y all by itself on one side of the equation. The easiest way to do that would be to add x to both sides, which cancels the -x on the left. We will be left with:
[tex] 3y=x+6 [/tex]
However, we can't have the coefficient of 3 on the variable y, or it won't be in slope-intercept form. So, we must divide both sides by 3.
[tex] \frac{3y}{3}=\frac{x}{3}+\frac{6}{3} [/tex]
[tex] y=\frac{x}{3}+2 [/tex]
Simplify.
[tex] y=\frac{1}{3}x+2 [/tex]
Useful note: [tex] \frac{x}{3}[/tex] is the same as [tex] \frac{1}{3}x[/tex]. This goes with any other fraction as well.
