1313_section3o1 - The slope of the dashed line is 5 2-3-2-1...

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1 Section 3.1 - Graphing Systems of Linear Inequalities in two Variables A linear equation in two variables x and y, ax + by + c = 0 has a solution set that can be exhibited graphically as points on a straight line. In this section, we will show that there is also a simple graphical explanation for linear inequalities in two variables. Let’s begin with a specific example. Example 1 . Graph y < 2 x + 6 . The graph of a given linear inequality is one of the half-planes, which are obtained as a result of the division of xy-plane by the line that represents the equation. The graph of two (or more) linear inequalities is the intersection region of these half-planes. Example 2. Graph the following system of inequalities and determine their solution set: 4 1 2 + + y x y x
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2 Example 3: Graph the following system of inequalities. a. 1 6 + - y x y x b. 0 9 3 6 2 3 < - + x y x y x
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3 -4 -3 -2 -1 1 2 3 4 5 -1 1 2 3 x y Example 4: Write a system of linear inequalities that describes the shaded region. a. b.
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4 c. The slope of the solid line with positive slope is 1.
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Unformatted text preview: The slope of the dashed line is 5 2-. -3-2-1 1 2 3 4 5 6-1 1 2 3 x y Example 5: Which of the following are true ? I. The point 16 3 , 10 7 is on the graph of . 6 2 10-y x II. The following two lines are perpendicular to each other. . 2 , 5 6 and 6) (4, through passes : Line 5 5 2 : Line 2 1 = +-L y x L III. A line through (3, 4) and (3, 5) is a horizontal line. IV. The line 2 2-= x y rises to the left. V. The point (1, -3) is a point in the solution set of x > 0 and ≤ y . Example 6: Which of the following are false ? I. The slope of the line through (3, -2) and (5, -2) is undefined. II. The point , 4 5 is on the graph of . 5 7 4-y x III. Line 1 L has slope m . Line 2 L is parallel to line 1 L , so 2 L has slope m-. IV. The point (1, 2) is in the solution set of 1--x y . V. The solution to 4 3 2 ≥--y x is the half-plane lying below the line 4 3 2 =--y x ....
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1313_section3o1 - The slope of the dashed line is 5 2-3-2-1...

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