slope y-intercept form is: y=mx+b
All you have to do is rearrange the equation:
2x-3y=6
2x=6+3y
2x-6=3y
now divide both sides by 3
(2x/3)-(6/3)=(3y/3)
and it becomes
[tex]y= \frac{2}{3}x-2 [/tex]x
Bonus: you can plug in any two values for x and y and you can see both equation gives the same answer!