Question 368689: Recently, I had to graph the inequality, y>1/2x-3, (Note: The less than symbol suppose to have a line under it to make it, less than OR equal to). I have finished graphing the inequality, but I do not know what quadrants it passes through in the graph, and if includes the bounday line, or not?
Answer by neatmath(302)   (Show Source):
You can put this solution on YOUR website! If it has the less than or equal sign, or the greater than or equal sign, the graph will ALWAYS include the boundary line.
If the inequality has the < or > signs, the graph will NEVER include the boundary line.
As far as this specific question, once you have graphed it, just pick a single point on either side of the boundary line, and use the x and y values in place of the variables in the inequality.
If the inequality is true, then you shade that side of the graph.
If the inequality is false, then you shade the other side of the graph.
For example, if I choose the point (0,0) then the inequality will become:
0>=1/2*(0)-3 which simplifies to 0>=-3 which is true, since 0 is greater than -3.
Then I would just shade the part of the graph which includes the point (0,0).
I hope this helps!
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