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Unformatted text preview: Sec 1.3 Wednesday, February 03, 2010 11:40 PM Section1dot3 Page 1 LINEAR describes a mathematical expression in which all variables appear to the first power EX: 2 x + 5 y = 12 1.3.1 Wednesday, February 03, 2010 11:40 PM Section1dot3 Page 2 LINEAR describes a mathematical expression in which all variables appear to the first power EX: 2 x + 5 y = 12 EQUALITY this means that the expression contains an equals sign Graphically, a linear equality represents a line in the xy plane, cutting the plane in two 1.3.2 Wednesday, February 03, 2010 11:40 PM Section1dot3 Page 3 LINEAR describes a mathematical expression in which all variables appear to the first power EX: 2 x + 5 y = 12 EQUALITY this means that the expression contains an equals sign Graphically, a linear equality represents a line in the xy plane, cutting the plane in two EX: 2 x + 5 y < 12 This is a linear expression containing an inequality sign rather than an equals sign Graphically, a linear inequality defines one half of the plane 1.3.3 Wednesday, February 03, 2010 11:40 PM Section1dot3 Page 4 LINEAR describes a mathematical expression in which all variables appear to the first power EX: 2 x + 5 y = 12 EQUALITY this means that the expression contains an equals sign Graphically, a linear equality represents a line in the xy plane, cutting the plane in two EX: 2 x + 5 y < 12 This is a linear expression containing an inequality sign rather than an equals sign Graphically, a linear inequality defines one half of the plane A region defined by a linear inequality, i.e. those points ( x , y ) for which the inequality is true 1.3.4 Wednesday, February 03, 2010 11:40 PM Section1dot3 Page 5 LINEAR describes a mathematical expression in which all variables appear to the first power EX: 2 x + 5 y = 12 EQUALITY this means that the expression contains an equals sign Graphically, a linear equality represents a line in the xy plane, cutting the plane in two EX: 2 x + 5 y < 12 This is a linear expression containing an inequality sign rather than an equals sign Graphically, a linear inequality defines one half of the plane A region defined by a linear inequality, i.e. those points ( x , y ) for which the inequality is true Step 1: graph 2 x + y = 1 Using intercepts (0, 1) and (1/2, 0) OR Using the form y = mx + b , i.e. y = 2 x + 1 1.3.5 Wednesday, February 03, 2010 11:40 PM Section1dot3 Page 6 LINEAR describes a mathematical expression in which all variables appear to the first power EX: 2 x + 5 y = 12 EQUALITY this means that the expression contains an equals sign Graphically, a linear equality represents a line in the xy plane, cutting the plane in two...
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This note was uploaded on 06/07/2011 for the course MATH 125 taught by Professor Tom during the Fall '07 term at University of Illinois at Urbana–Champaign.
 Fall '07
 Tom
 Math, Linear Algebra, Algebra

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