+ Lesson 6-5 Linear Inequalities November 17, 2014

+ Daily Learning Target I will graph linear inequalities in two variables. I will use linear inequalities when modeling real-world situations.

+ Vocabulary Linear inequality Describes a region of the coordinate plane that has a boundary line Solution of an inequality Coordinates of the plane that makes the inequality true

Tell whether the ordered pair is a solution of the inequality. Example 1: In Notes (–2, 4); y < 2x + 1

Tell whether the ordered pair is a solution of the inequality. Independent Practice #1 (3, 1); y > x – 4

Graphing Linear Inequalities Step 1 Solve the inequality for y (slope-intercept form). ( y=mx+b) Step 2 Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for. Step 3 Shade the half-plane above the line for y > or ≥. Shade the half-plane below the line for y < or y ≤. Check your answer.

Graph the solutions of the linear inequality. Example 2: Write in your Notes y  2x – 3 Step 1 The inequality is already solved for y. Step 2 Graph the boundary line y = 2x – 3. Use a solid line for . Step 3 The inequality is , so shade below the line.

+ Independent Response How do you know when you shade above or below the boundary line? When do you use a dotted boundary line? When do you use a solid boundary line?

Independent Practice #2 Graph the solutions of the linear inequality. Check your answer.

Write an inequality to represent the graph. Example 3: Writing an Inequality from a Graph

Write an inequality to represent the graph. Independent Practice #3

+ Special Cases Y> 3 Zero slope X< -2 Undefined slope

Graph the solutions of the linear inequality. Check your answer. Ex 4: Graphing in Standard Form Write this in your notes 5x + 2y > –8

For a party, you can spend no more than $12 on nuts. Peanuts cost $2/lb. Cashews cost $4/lb. What are three possible combinations of peanuts and cashews you can buy? Word Problem!: Notes a. Write a linear inequality to describe the situation.

Ada has at most 285 beads to make jewelry. A necklace requires 40 beads, and a bracelet requires 15 beads. Word Problem!: Independent Practice #4 a. Write a linear inequality to describe the situation. Let x represent the number of necklaces and y the number of bracelets. Write an inequality. Use ≤ for “at most.”