The x- and y-intercepts are both zero, so you can't use intercepts to draw this graph. You only need two points to draw the graph, so plug in any value for x other than zero. y=-x so you can find y. Mark this point. Repeat for another value of x and find the corresponding y. Draw a line through these two points. It will pass through the origin.
Example: let x=5, then y=-5, plot A(5,-5); let x=-5 then y=-(-5)=5, plot B(-5,5). The line AB is a segment of y=-x, so you need to draw the line through both points. You will get a 45° line (leaning backwards).