Yes, we can graph -x-4y > 3 in that form, though your teacher may have
intended you to solve it for y, which is an alternate way, which is used
by some teachers. If you were taught that way, let me know in the thank-you
note and I'll redo it using that method.
First we form the equation of the boundary line, which is just
like the inequality except that it has an = instead of the inequality >
The boundary line's equation is -x-4y = 3
We find some points on that line (-3,0), (1,-1) and (5,-2),
and we draw the line through them dotted instead of solid because the
inequality is >, not 
, so equality is not included, and
since the line's equation has an = sign, it is not included in the
symbol >.
Now that we have graphed the boundary line, we have to find out which
side of that line the solutions are on/ So we pick a point off the line
and test it to see if it is a solution or not. If it tests true, then
that test point is a solution, so whichever side it is on is the side
on which ALL the solutions lie. If the test point tests false, then the
solutions are NOT on the same side as the test point, so we know they are
on the other side, so we shade it.
Since the origin (0,0) does not lie on the line, it will be the easiest
point to choose as a test point, because zero is the easiest number of
all to substitute.
So we test (0,0) by substituting x=0 and y=0 into the original inequality:
-x-4y > 3
-(0)-4(0) > 3
0-0 > 3
0 > 3
That is false, so the origin is not a solution, so the solutions are all
on the side of the line which the origin is not on, so we shade the lower
side of the line, since the origin (0,0) is on the upper side of the line:
So the solution set for the inequality is the set of points shaded in green
below:
Edwin
