The easiest way to solve this is to first solve for y to get this in slope intercept form y=mx+b
subtract x from both sides
4y= -x-4
divide both sides by 4
y= -1/4x -1
since this is in slope intercept form we know that when with y=mx+b that m is the slope and b is the y intercept
our b value for this is -1 so our slope is -1
You can also solve this by plugging 0 in for x and solving for y. This will also give you the y intercept.
0 + 4y=-4
divide both sides by 4
y=-1. So when x=0, y=-1. Either way you get the same answer. The Y intercept is -1