SOLUTION: Please help explain graphing inequalities! Thanks! I understand how to find out how to place the "line" what is stumping me is how to figure out which side of the line to shade

Algebra ->  Inequalities -> SOLUTION: Please help explain graphing inequalities! Thanks! I understand how to find out how to place the "line" what is stumping me is how to figure out which side of the line to shade      Log On


   

Question 77595: Please help explain graphing inequalities! Thanks!
I understand how to find out how to place the "line" what is stumping me is how to figure out which side of the line to shade! My equation is x%3C1-y and I figured out where to place the "line" on the graph, I am confused on how to figure out which side of the line (top or bottom) to shade.
Thank You!
Josh
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x<1-y
y<-x+1
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C-x%2B1%29
That is the graph of the EQUALITY.
y<-x+1 is above or below it.
Pick any point that is not on the line, like (0,5)
That is your "test point".
Substitute the x,y values into the INEQUALITY:
5<-0+1
5<1
That is false.
So the half-plane containing that test point is NOT
the graph of the INEQUALITY. The other half plane
IS the solution.
--------
If you had selected the test point (3,-10)
you would have substituted and gotten:
-10<-3+1
-10<-2
That is true
So the half-plane containing that test point IS
the graph of the INEQUALITY.
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Hope this helps.
Cheers,
Stan H.