Daily Homework Quiz Solve the inequality. Then graph the solution. 9 ≤ +– 4x4x712x x 8 0 or 3x <> ANSWER –––––– ≥ x–2 x 2 – –––––

4.2 Solving Linear Inequalities in 2 Variables 11/5/2012 Goal : Solve and graph linear inequalities in two variables.

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.

Example 1 Check Solutions of Inequalities () 1, 4 a.b. 2, 1 () – ORDERED PAIR SOLUTION a. () 1, 4 2, 1 () – b. () = < 35 –1 () 2, 1 () – is a solution. < 2x y + 5 () = < 65 SUBSTITUTE () 1, 4 is not a solution. CONCLUSION Check whether the given ordered pair is a solution of.

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

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

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.

Example 3 Graph Linear Inequalities in Two Variables Graph. 2x2xy < – 8 3x3x2y2y ≥

Graphing Horizontal Line Inequality Ex: y > -2 Ex: y ≤ 3

Graphing Vertical Line Inequality Ex: x > -2 Ex: x ≤ 3

Checkpoint Graph the inequality in a coordinate plane. Graph Linear Inequalities in One Variable ANSWER 9. ANSWER x > 1 – 10. y ≥ 1

Checkpoint Graph the inequality in a coordinate plane. Graph Linear Inequalities in One Variable ANSWER 11. ANSWER y ≤ 3 – 12. < x4

Homework WS 4.2