SOLUTION: Hi, my final question is : Graph and shade,2x>-6y. What I did was plug in 1 for x and y and I got an answer of 2>-6, which is true. Again thank you for your help

Algebra ->  Algebra  -> Graphs -> SOLUTION: Hi, my final question is : Graph and shade,2x>-6y. What I did was plug in 1 for x and y and I got an answer of 2>-6, which is true. Again thank you for your help      Log On

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Question 86566: Hi,
my final question is : Graph and shade,2x>-6y. What I did was plug in 1 for x and y and I got an answer of 2>-6, which is true. Again thank you for your help
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
First we need to graph the equation 2x=-6y (just replace the inequality sign with an equal sign)

%282x%29%2F-6=y Divide both sides by -6

y=%28-1%2F3%29x Reduce

So here's the graph of y=%28-1%2F3%29x

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F3%29x%29+

Now lets pick a test point, any will do. I'm going to use your test point (1,1). Now evaluate the test point with the inequality:

2%281%29%3E-6%281%29 Plug in x=1 and y=1 into the inequality

2%3E-6 Multiply

Since this inequality is true, we simply shade the region that contains (1,1):

note: since the inequality is a greater than sign, we do not include the boundary. So the red line should be a dashed line.
drawing%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%281%2C1%2C0.08%29%2C%0D%0Acircle%281%2C1%2C0.1%29%2Cgraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B1%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B2%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B3%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B4%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B5%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B6%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B7%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B8%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B9%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B10%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B11%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B12%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B13%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%28-1%2F3%29x%2Asqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%2C+%28-1%2F3%29x%2B14%29%29 graph of the inequality 2x%3E-6y with the boundary in red and the shaded region in green. Notice the test point lies in the shaded region.