# SOLUTION: how can I graphed the boundary line for the linear inequality and Determine the correct half–plane and complete the graph. y<2x-6

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 Question 91262: how can I graphed the boundary line for the linear inequality and Determine the correct half–plane and complete the graph. y<2x-6Answer by jim_thompson5910(28593)   (Show Source): You can put this solution on YOUR website!In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (note: if you need help with graphing, check out this solver) graph of Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,0) into the inequality Plug in and Simplify (note: for some reason, some of the following images do not display correctly in Internet Explorer. So I would recommend the use of Firefox to see these images.) Since this inequality is not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line Graph of with the boundary (which is the line in red) and the shaded region (in green) (note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)