Question 550015: Can you explain why a point on the boundary line cannot be used as a test point when graphing a linear inequality in two variables? Also please give me an example, thank you.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Let's say your inequality is  or  .
We know that the points (0,6), and (6,0) are part of the boundary line  which is part of the solution for the first inequality above, but not for the other.
We know that the points to one side of that line are part of the solution, and the points to the other side are not part of the solution. We have to find which side is which.
For an easy way to figure out which side is part of the solution we choose a test point that is to one side of the line, and see if it is a solution or not. Either way, that tells us which side is part of the solution.
Choosing a test point on the line does not tell us which side of the line is the solution. At most, it whether a point on the line is part of the solution, but we knew that already. If the inequality symbol includes an "or equal" the line belongs to the solution; if the inequality symbol is just greater than or lesser than, the line is not part of the solution. We do not need a test point for that part.
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