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**2.7 Two-Variable Inequalities**

Graphing Linear Inequalities Graphing Absolute-Value Inequalities

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**1) Graphing Linear Inequalities**

The graph of a linear inequality is a region of the coordinate plane that is bounded by a line

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**1) Graphing Linear Inequalities**

What it shows… the values on the coordinate plane that apply to the function What an equation looks like…

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**1) Graphing Linear Inequalities**

What it shows… the values on the coordinate plane that apply to the function What an equation looks like… Inequality symbol Slope y-intercept

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**1) Graphing Linear Inequalities**

What linear inequality graphs look like… 1) boundary line (solid or dashed) 2) shaded area (above or below the boundary line)

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**1) Graphing Linear Inequalities**

A dashed boundary line means the line is NOT part of the solution The shading is ABOVE the boundary line if the equation is of the form y > OR y > y < OR y >

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**1) Graphing Linear Inequalities**

A solid boundary line means the line IS part of the solution The shading is BELOW the boundary line if the equation is of the form y < OR y < y < OR y >

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**1) Graphing Linear Inequalities**

Example 1: Graph the inequality y < 2x + 2

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**1) Graphing Linear Inequalities**

Remember… y = mx + b Example 1: Graph the inequality y < 2x + 2

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**1) Graphing Linear Inequalities**

Remember… y = mx + b Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2

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**1) Graphing Linear Inequalities**

Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2

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**1) Graphing Linear Inequalities**

Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2

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**1) Graphing Linear Inequalities**

Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2

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**1) Graphing Linear Inequalities**

Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2 y < DASHED line

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**1) Graphing Linear Inequalities**

Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2 y < SHADE BELOW the line

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**1) Graphing Linear Inequalities**

Example 2: Write an inequality for the graph below.

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**1) Graphing Linear Inequalities**

Example 2: Write an inequality for the graph below. y = mx + b y –int = m = inequality type

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**1) Graphing Linear Inequalities**

Example 2: Write an inequality for the graph below. y = mx + b y –int = m = inequality type

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**1) Graphing Linear Inequalities**

Example 2: Write an inequality for the graph below. y = mx + b y –int = -3 m = inequality type

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**1) Graphing Linear Inequalities**

Example 2: Write an inequality for the graph below. y = mx + b y –int = -3 m = -3/2 inequality type >

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**1) Graphing Linear Inequalities**

Example 2: Write an inequality for the graph below. y –int = -3 m = -3/2 inequality type > Sub into y > mx + b

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**1) Graphing Linear Inequalities**

Example 2: Write an inequality for the graph below. y –int = -3 m = -3/2 inequality type > Sub into y > mx + b y > -3x/2- 3

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**Homework p.104 #1, 5, 7, 20, 21, 23, 26, 37, 38 Don’t forget…**

Quiz TUESDAY Test FRIDAY

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**2) Absolute Value Inequalities**

Graph the absolute value function then shade above OR below

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**2) Absolute Value Inequalities**

Graph the absolute value function then shade above OR below Solid line…y <, y> Dashed line…y<, y> Shade above y>, y> Shade below…y<, y<

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**2) Absolute Value Inequalities**

Example 1: Graph y < |x – 2| + 3

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**2) Absolute Value Inequalities**

Example 1: Graph y < |x – 2| DASHED line Shade BELOW slope = 1 Vertex = (2, 3)

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**2) Absolute Value Inequalities**

Example 1: Graph y < |x – 2| slope = 1 DASHED line Shade BELOW Vertex = (2, 3)

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**2) Absolute Value Inequalities**

Example 1: Graph y < |x – 2| slope = 1 DASHED line Shade BELOW Vertex = (2, 3)

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**2) Absolute Value Inequalities**

Example 1: Graph y < |x – 2| slope = 1 DASHED line Shade BELOW Vertex = (2, 3)

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**2) Absolute Value Inequalities**

Example 1: Graph y < |x – 2| slope = 1 DASHED line Shade BELOW Vertex = (2, 3)

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**2) Absolute Value Inequalities**

Example 1: Graph y < |x – 2| slope = 1 DASHED line Shade BELOW Vertex = (2, 3)

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**2) Absolute Value Inequalities**

Example 2: Graph –y + 1 < -2|x + 2|

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**2) Absolute Value Inequalities**

Example 2: Graph –y + 1 < -2|x + 2| -y < -2|x + 2| - 1 y > 2|x + 2| + 1 -y so CHANGE the direction of the inequality

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**2) Absolute Value Inequalities**

y > 2|x |

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**2) Absolute Value Inequalities**

y > 2|x | Slope = 2 Solid line Shade above Vertex = (-2, 1)

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**2) Absolute Value Inequalities**

y > 2|x |

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**2) Absolute Value Inequalities**

y > 2|x |

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**2) Absolute Value Inequalities**

y > 2|x |

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**2) Absolute Value Inequalities**

y > 2|x |

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**2) Absolute Value Inequalities**

Example 3: Write an equation for the graph below.

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**Homework p.104 #11-13, 22, 30, 39-42 Reminders…**

Quiz TUESDAY (2.5, 2.6, first half 2.7) Review WEDNESDAY, THURSDAY Test FRIDAY (Chapter 2 ONLY) Extra-help WEDNESDAY at LUNCH

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