Question 144432
2x+3y<=6 
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This is both an EQUALITY and an INEQUALITY.
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You ALWAYS need to graph the EQUALITY first because
it is the boundary of the inequality.
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2x+3y = 6
Let x=0, then y = 2 giving you point (0,2)
Let y=0, then x = 3 giving you point (3,0)
Plot those two points and draw a line thru them.
That is the graph of the EQUALITY.
{{{graph(400,300,-10,10,-10,10,(-2/3)x+2)}}}
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Since your INEQUALITY states 2x+3y is Less than 6,
shade the half-plane BELOW the boundary line. That
is the graph of the INEQUALITY.
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The union of the two graphs is the graph for your problem.
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Cheers,
Stan H.