Answer: None of the lines are parallel to one another
======================================================
Step-by-step explanation:
Solve each equation for y
Line a:
4y+x = 8
4y = -x+8
y = (-x+8)/4
y = (-x/4) + (8/4)
y = (-1/4)x + 2
This equation is in the form y = mx+b with slope m = -1/4
---------------
Line b:
2y+x = 4
2y = -x+4
y = (-x+4)/2
y = (-x/2) + (4/2)
y = (-1/2)x + 2
The slope is m = -1/2. It is not parallel to line a because parallel lines must have the same slope (but different y intercept).
-----------------
Line c:
2y = -3x+6
y = (-3x+6)/2
y = (-3x/2) + (6/2)
y = (-3/2)x + 3
The slope here is m = -3/2. it is not parallel to line a, and it is not parallel to line b either for similar reasons discussed above.
-----------------
In summary, none of the three lines are parallel to one another. The graph below visually confirms this. Each pair of lines intersects at exactly one location, showing they cannot be parallel.