SOLUTION: I don't understand how to graph an inequality. Would someone please help me? 2x+3y<=6 I don't understand how to get the points to graph. Thank you!

Algebra ->  Inequalities -> SOLUTION: I don't understand how to graph an inequality. Would someone please help me? 2x+3y<=6 I don't understand how to get the points to graph. Thank you!      Log On


   

Question 144432: I don't understand how to graph an inequality. Would someone please help me?
2x+3y<=6 I don't understand how to get the points to graph. Thank you!
Found 2 solutions by nabla, stanbon:
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
2x+3y<=6
3y<=6-2x
y<=2-(2/3)x
Plot that function as normal (y intercept=2; the graph goes DOWN 2 and TO THE RIGHT 3 for each whole number plot point because of the slope). Now, where is the function valued less than or equal to that line? Just shade below the line.
graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+2-%282%2F3%29x+%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28-2%2F3%29x%2B2%29
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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.