Question 151026
Wow, that's a lot of writing.
Your fingers must be tired. 
I'll do three of your problems.
1.{{{x+3y=6}}}
{{{3y=-x+6}}}
{{{y=(-x+6)/3}}}
Slope = -(1/3)
Y-intercept = (0,2)
{{{drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),green(line(-18,8,18,-4)))}}}
2.{{{x=2}}}
A vertical line at x=2.

{{{drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),green(line(2,-20,2,20)))}}}
3.{{{y=-1}}}
A horizontal line at y=-1.

{{{drawing( 300, 300, -5, 5, -5, 5,grid( 1 ),green(line(-20,-1,20,-1)))}}}