Question 57646: Show how a test point for the inequality 3x+y >= 6 tells which side will be shaded. (Show the test point results and explain what that means)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 3x+y >= 6 tells which side will be shaded. (Show the test point results and explain what that means)
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Graph y=-3x+6 passing thru (0,6) and (1,3)
That would take care of the iquality.
Now, where is y>-3x+6
Since the y is greater than the y values must
be above the equality line.
Test a point that is above the line like (0,10)
Substitute that pair of x y values into the
inequality and see if the values satisfy the
inequality:
10>-3(0)+6
10>6
That is true; that means any point you would
pick above the line of the equality would
satisfy the inequality.
Also, any point you would pick below the
line would fail to satisfy the inequality.
Try (1,1) which is below (1,3)
3>-3(1)+6
3>3
That is incorrect; that means points below
the equality line do not satisfy the inequality.
Hope this helps.
Cheers,
Stan H.
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