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Graph `x+y<-1` :
The graph will show the solution set to the inequality; i.e. every point that is a solution. The solution set is a half-plane.
Begin by sketching the graph of x+y=-1 **Note: you will sketch this in as a dotted line. The inequality is a strict inequality so no points on the line satisfy the inequality. If the inequality had been `x+y<=-1` you would draw a solid line.
Next test a point not on the line. In this case the origin is not on the line. So we check; is 0+0<-1? Since it is not, no point on the same side of the line as (0,0) is a solution, so you shade the other side (heading "down" and to the "left".)
The grapher will not show the shading: here is the graph of the line
If you have Java enabled, you might try the site gcalc which is a graphing calculator emulator. This would enable you to see the graph as a shaded half-plane.
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