SOLUTION: I have to graph inequalities in two variables, and pick a point in each half plane. After, I have to test the points to see if they are true or false. Will someone help me graph th

Algebra ->  Graphs -> SOLUTION: I have to graph inequalities in two variables, and pick a point in each half plane. After, I have to test the points to see if they are true or false. Will someone help me graph th      Log On


   

Question 124640: I have to graph inequalities in two variables, and pick a point in each half plane. After, I have to test the points to see if they are true or false. Will someone help me graph them?
y<-1/2x-3
2x-3y<6
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
graph inequalities in two variables, and pick a point in each half plane. After, I have to test the points to see if they are true or false. Will someone help me graph them?
y<-1/2x-3
2x-3y<6
--------------
You start by graphing the boundaries:
y = (-1/2)x-3 ; this is the boundary of y<(-1/2)x-3
and
y = (2/3)x-2 ; this is the boundary of y>(2/3)x-2
----------------
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28-1%2F2%29x-3%2C%282%2F3%29x-2%29
----------------
You now have four half-planes---one on each side of each of the lines.
-------------------
Consider the boundary of y < (-1/2)x-3
Test point above the line: (0,0)
0 < (-1/2)*0-3; false
-----------------
Test point below the line: (0,-4)
-4 < (-1/2)*0 -3; true
-------------------------------
Consider the boundary of y>(2/3)x-2
Test point above the line: (0,0)
0 > (2/3)*0 -2; true
-------
Test point below the line: (0,-4)
-4 > (2/3)*0 -3 ; false
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Cheers,
Stan H.