4x + y = 0 write that in slope intercept form

Slope intercept form is y=mx+b, where m is slope and b is the y-intercept.
So, to achieve that form, you have to move 4x to the other side. You do this by subtracting both sides of the equation by 4x. When you do that, you will have:
y=-4x+0

Because there is no number next to y, there is nothing else for you to do here. The equation is now in slope-intercept form. The slope of the equation is -4/1 (remember rise/run) and the line intersects the y-axis at point (0,0).

Hope this helps :-)