2-7 Two-Variable Inequalities M11.D.2.1.2: Identify or graph functions, linear equations, or linear inequalities on a coordinate plane

Objectives Graphing Linear Inequalities Graphing Two-Variable Absolute Value Inequalties

Vocabulary A linear inequality is an inequality in two variables whose graph is a region of the coordinate plane that is bounded by a line. A solid boundary line means the line is part of the solution. ex. ≥ or ≤ A dashed boundary line means the line is not part of the solution. ex. > or <

Vocabulary To figure out whether to shade above or below the line, Solve first for y. If y is greater or greater than or equal to the line, you shade above. ex. y > 2x + 1 If y is less than or less than or equal to the line, you shade below. ex. y ≤ 2x + 1

Step 1: Graph the boundary line y = x + 1. Since the inequality is greater than, not greater than or equal to, use a dashed boundary line Graph y > x Step 2: Since the inequality is greater than, y-values must be more than those on the boundary line. Shade the region above the boundary line. Graphing a Linear Inequality

A restaurant has only 15 eggs until more are delivered. An order of scrambled eggs requires 2 eggs. An omelet requires 3 eggs. Write an inequality to model all possible combinations of orders of scrambled eggs and omelets the restaurant can fill till more eggs arrive. Graph the inequality. Relate: plus is less than or equal to number of eggs needed for x orders of scrambled eggs number of eggs needed for y orders of omelets 15 Define: Let x = the number of orders for scrambled eggs. Let y = the number of orders for omelets. Write: 2 x+3 y < – Real World Example

(continued) Step 1: Find two points on the boundary line. Use the points to graph the boundary line. when x = 0, 2(0) + 3y = 15 3y = 15 y = 5 when y = 0, 2x + 3(0) = 15 2x = 15 x = 15 2 Graph the points (, 0) and (0, 5). Since the inequality is less than or equal to, use a solid boundary line Continued

(continued) Step 2: Since the inequality is less than, y-values must be less than those on the boundary line. Shade the region below the boundary line. All ordered pairs with whole-number coordinates in the shaded area and on the boundary line represent a combination of x orders of scrambled eggs and y orders of omelets that the restaurant could fill. Continued

Graph y |2x| – 3. Since the inequality is greater than or equal to, the boundary is solid and the shaded region is above the boundary. > – Graphing Absolute Value Inequalities

Write an inequality for each graph. The boundary line is given. a.Boundary: y = | x – 2| – 1 The boundary line is dashed. The shaded region is above the boundary. This is the graph of y > |x – 2| – 1. b.Boundary: y = – x The boundary is solid. The shaded region is below the boundary. This is the graph of y – x < – Writing Inequalities

Homework Pg 104 & 105 # 1,2,10,11,12,20,21