Slope-intercept form is y=mx+b, where m is the slope, and b is the y-intercept.
So, to convert x+6y=-2, you have to isolate y. Your first step is to move the x to the other side. To do this, you subtract 1x from both sides:
6y=-x-2
Your final step is to divide both sides by 6:
y=-1/6x+1/3
Hope this helps :-)