Question

what is the parallel to 2x-3y=6 and passing through(-3,1)

Answer 1

y=2/3+3

Answer 2

The slope of the parallel line will be the same as the slope from from the given line. if you pu tthe given line into y=mx+b form, you can read the slope, m.
2x-3y=6
2x-6=3y
y=(2/3)x-2
So the slope of the line is m=2/3.
Now you have a point and the slope, so you can use the point-slope formula to find the line:
y-1=(2/3)(x+3)
y=(2/3)x+2+1
or
y=(2/3)x+3

Answer 3

I give you better clue ax+by+c=0 for this equation slope=-a/b
for parallel line obviously you will have same slope as this line
and when you have a slope and point then you can easily put in point slope form y-y1=m(x-x1)