+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 inequalityCoordinates 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 2Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for < or >.

Step 3Shade 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> 3Zero slope

X< -2Undefined 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.”