SOLUTION: Describe the graph of 3x+y<1 a) a dotted line with shading below the boundary line 3x+y=1 b) a solid line with shading abouve the boundary line 3x+y=1 c) a solild line wtih shad

Question 100854: Describe the graph of 3x+y<1
a) a dotted line with shading below the boundary line 3x+y=1
b) a solid line with shading abouve the boundary line 3x+y=1
c) a solild line wtih shading below the boundary line 3x+y=1
d) a dotted line with shading above the boundary line 3x+y=1
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Describe the graph of 3x+y<1
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Solve for y: y <-3x+1
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The boundary of the solution set is y=3x+1

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Take a test point that is not on the boundary, like (0,0)
Substitute the x and y values of the test point into the
inequality: 0 < 0 +1
This is false, so the half-plane solution set for the
inequality is on the side of the boundary that does not
contain (0,0)-------------that would be the half-plane
above the boundary line.
---------------
Note the boundary line is NOT part of the solution set because
equality is not stated in the original equation.
-----------------------
The solution is "d".
--------------------------
Cheers,
Stan H.
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