SOLUTION: When graphing the inequality 3x-2y≥ 0, why can’t we use (0, 0) as a test point/ If we test the point (-4, 2), do we obtain a false statement or true one?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: When graphing the inequality 3x-2y≥ 0, why can’t we use (0, 0) as a test point/ If we test the point (-4, 2), do we obtain a false statement or true one?      Log On


   

Question 642887: When graphing the inequality 3x-2y≥ 0, why can’t we use (0, 0) as a test point/ If we test the point (-4, 2), do we obtain a false statement or true one?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
you are given:
3x-2y+%3E=0}
that inequality simplifies to:
3x+%3E=+2y....=>...2y%3C=3x+=>...y%3C=%283%2F2%29x+

The boundary of the inequality is y+=+%283%2F2%29x
The point (0,0) is on the boundary line. It satisfies the
equality but cannot be used to test the inequality because it is on+the boundary+line.
You have to use a test point that is not on the boundary+line.
Using (-4, 2) you get 2%3C=%283%2F2%29%28-4%29+...=>...2%3C=%283%2A%28-4%29%2F2%29+..=>...2%3C=%28-12%29%2F2%29+
=>...2%3C=-6+
That is not true so the half-plane does containing (-4, 2) is not the solution set for the inequality.
Solved by pluggable solver: Plot Any Inequality
Graphing function y%3C=%283%2F2%29x:

graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+y%3C=%283%2F2%29x+%29


as you can see (when you plot it) this point (-4, 2) is not the solution set for the inequality