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Daily Homework Quiz Solve the inequality. Then graph the solution. 9 ≤ +– 4x4x712x 1. + 2. 2x 8 0 or 3x 5 11 + <> ANSWER 0123. 432165 –––––– ≥ x–2 x 2 – 24686420108 –––––
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4.2 Solving Linear Inequalities in 2 Variables 11/5/2012 Goal : Solve and graph linear inequalities in two variables.
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In this section, we’re going to graph inequalities written in the form: y > mx + b, y < mx + b, y ≥ mx + b, y ≤ mx + b A point (x, y) is a solution if and only if the inequality is TRUE when the value of x and y are substituted into the inequality.
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Example 1 Check Solutions of Inequalities () 1, 4 a.b. 2, 1 () – ORDERED PAIR SOLUTION a. () 1, 4 2, 1 () – b. () 2 2 + = < 35 –1 () 2, 1 () – is a solution. < 2x y + 5 () 1 2 + 4 = < 65 SUBSTITUTE () 1, 4 is not a solution. CONCLUSION Check whether the given ordered pair is a solution of.
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Checkpoint Check Solutions of Inequalities Check whether the given ordered pair is a solution of 4.4. > x 3y – () 0, 0 1. ANSWER not a solution 2. 4, 1 () – ANSWER solution 3. 2, 2 () –– ANSWER not a solution 4. 3, 5 () – ANSWER solution
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Graphing a Linear Inequality 1.) Draw the boundary line: y=mx+b For > or <, dashed line For ≤ or ≥, solid line 2.) Shade the half plane. (inequality must be written in slope intercept form Above: > or ≥ Below: < or ≤ Above Below: Above Below Positive Slope Negative Slope Boundary line
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2. Shade the half plane (textbook way) Test a point (x, y) not on the boundary line and see if it is a solution. If it is, shade the side that contains that point. If it is not, shade the other side.
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Example 3 Graph Linear Inequalities in Two Variables Graph. 2x2xy < – 8 3x3x2y2y ≥
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Graphing Horizontal Line Inequality Ex: y > -2 Ex: y ≤ 3
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Graphing Vertical Line Inequality Ex: x > -2 Ex: x ≤ 3
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Checkpoint Graph the inequality in a coordinate plane. Graph Linear Inequalities in One Variable ANSWER 9. ANSWER x > 1 – 10. y ≥ 1
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Checkpoint Graph the inequality in a coordinate plane. Graph Linear Inequalities in One Variable ANSWER 11. ANSWER y ≤ 3 – 12. < x4
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Homework WS 4.2
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