basically
y=mx+b
solve for y
a.
3x+4y-12=0
add -3x+12 to both sides
4y=-3x+12
divide both sides by 4
y=-3/4x+3
slope=-3/4, yint=3
b.
2x+y=1
minus 2x both sides
y=-2x+1
slope=-2, yint=1
c.
2x-y=4
minus 2x both sides
-y=-2x+4
times -1 both sides
y=2x-4
slope=2, yint=-4
d.
2x-y=0
minus 2x both sides
-y=-2x
times -1
y=2x+0
slope=2, yint=0
e.
x+3y=0
minus x both sides
3y=-x
divide by 3
y=-1/3x+0
slope=-1/3, yint=0
f.
2y-6=0
add 6 both sides
2y=6
divide both sides by 2
y=3
y=0x+3
slope=0, yint=3