SOLUTION: Graph 2x+3y<=6

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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


Since this inequality is true, we simply shade the entire region that contains (0,0)

Graph of with the boundary (which is the line in red) and the shaded region (in green)