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**Chapter 6 – Solving and Graphing Linear inequalities**

6.5 – Graphing Linear Inequalities in Two Variables

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**6.5 – Graphing Linear Inequalities in Two Variables**

Today we will be learning how to: Graph a linear inequality in two variables Model a real-life situation using a linear inequality in two variables

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**6.5 – Graphing Linear Inequalities in Two Variables**

A linear inequality in x and y is an inequality that can be written with >, ≥, <, or ≤.

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**6.5 – Graphing Linear Inequalities in Two Variables**

An ordered pair (x, y) is a solution of a linear inequality when the values of x and y are substituted into the inequality and the result is true.

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**6.5 – Graphing Linear Inequalities in Two Variables**

Example 1 Check whether the ordered pair is a solution of 4x + 5y ≤ 12. (-3, 5) (0, 2) (6, -8)

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**6.5 – Graphing Linear Inequalities in Two Variables**

The graph of a linear inequality in two variables is the graph of the solutions of the inequality. The graph of 2x – 3y ≥ -2 is shown. Every point in the shaded region and on the line is a solution of the inequality. Every other point is not a solution.

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**6.5 – Graphing Linear Inequalities in Two Variables**

GRAPHING A LINEAR INEQUALITY Graph the corresponding equation (y = mx + b) Use a dashed line for inequalities with > or < Use a solid line for inequalities with ≥ or ≤. The line you drew separates the coordinate plane into two half-planes. If the symbol is > or ≥, shade above the line. If the symbol is < or ≤, shade below the line.

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**6.5 – Graphing Linear Inequalities in Two Variables**

Example 2 Sketch the graph of x ≥ 1.

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**6.5 – Graphing Linear Inequalities in Two Variables**

Example 3 Sketch the graph of y > -3.

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**6.5 – Graphing Linear Inequalities in Two Variables**

Example 4 Sketch the graph of x – y ≤ 2.

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**6.5 – Graphing Linear Inequalities in Two Variables**

Example 5 Sketch the graph of y + x > -1.

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**6.5 – Graphing Linear Inequalities in Two Variables**

HOMEWORK Page 363 #24 – 52 even

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**6.5 – Graphing Linear Inequalities in Two Variables**

HOMEWORK Page 364 #43 – 48, 50 – 60 even

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