MAT_1143-feb_23 - February 23, 2011 Click to edit Master...

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Click to edit Master subtitle style February 23, 2011 Sections 3.3
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Above and Below the Line Sometimes we are interested in the regions above and below the line Called a linear inequality Like: 2x + y < 4 Graph the line It divides the plane into 3 parts (above, below, and the line itself)
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Like: 2x + y < 4 Test a point on each side to decide which side gives us the solution (0,0) is not on the line, so let’s use it (0,0) A: Satisfies Ineq. B: Does not satisfy
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Get a whole region that is a solution Whether line itself is included depends on <, >, , For 2x + y < 4 A: use a solid line B: use a dashed line C: doesn’t really matter
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So for 2x + y < 4
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Other Direction Might be given the region shaded either above or below a line Can find equation of line as in chapter 2 Line is A: y = 1 + x B: y = 2 + x C: y = 1 + 2x D: y = 1 + ½x
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Test a point on the shaded side to decide which direction the inequality should go Inequality is A: y = 1 + 2x B: y > 1 + 2x C: y < 1 + 2x D: y ≤ 1 + 2x E. y ≥ 1 + 2x
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MAT_1143-feb_23 - February 23, 2011 Click to edit Master...

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