So the set of points (x,y,z) in 3D space satisfying x+y = 3 is the gray plane.
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Clean-up: close the above folder and hit the folder-icon.
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Goal 2: To plot, in 3D, the one inequality: x+y is less than or equal to 3 .
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Let's go to 2D viewpoint.
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Let's plot, from the 2D viewpoint, the set of point (x,y,z) in 3D space satisfying the equalities: x+y is less than or equal to 3 AND z=0.
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Expression 24: "x" plus "y" less than or equal to 3 left brace, "z" equals 0 , right bracex+y≤3z=0
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Let's go to 3D viewpoint.
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Let's plot some samples of x+y<3 AND z= some number. (Open folder.)
Hide this folder from students.
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Expression 27: "x" plus "y" less than or equal to 3 left brace, "z" equals 1.5 , right bracex+y≤3z=1.5
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Expression 28: "x" plus "y" less than or equal to 3 left brace, "z" equals 3 , right bracex+y≤3z=3
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Expression 29: "x" plus "y" less than or equal to 3 left brace, "z" equals negative 1.5 , right bracex+y≤3z=−1.5
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Expression 30: "x" plus "y" less than or equal to 3 left brace, "z" equals negative 3 , right bracex+y≤3z=−3
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So what does the set of ALL points (x,y,z) in 3D space R^3 satisfying the inequality x+y < or = to 3 look like? Let's graph (and click "Extend to 3D").
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Expression 32: "x" plus "y" less than or equal to 3x+y≤3
