 # 2.7 Two-Variable Inequalities

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2.7 Two-Variable Inequalities
Graphing Linear Inequalities Graphing Absolute-Value Inequalities

1) Graphing Linear Inequalities
The graph of a linear inequality is a region of the coordinate plane that is bounded by a line

1) Graphing Linear Inequalities
What it shows… the values on the coordinate plane that apply to the function What an equation looks like…

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

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)

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 >

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 >

1) Graphing Linear Inequalities
Example 1: Graph the inequality y < 2x + 2

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

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

1) Graphing Linear Inequalities
Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2

1) Graphing Linear Inequalities
Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2

1) Graphing Linear Inequalities
Example 1: Graph the inequality y < 2x + 2 y-int = 2 m = 2

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

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

1) Graphing Linear Inequalities
Example 2: Write an inequality for the graph below.

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

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

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

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

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

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

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

2) Absolute Value Inequalities
Graph the absolute value function then shade above OR below

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<

2) Absolute Value Inequalities
Example 1: Graph y < |x – 2| + 3

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

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

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

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

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

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

2) Absolute Value Inequalities
Example 2: Graph –y + 1 < -2|x + 2|

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

2) Absolute Value Inequalities
y > 2|x |

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

2) Absolute Value Inequalities
y > 2|x |

2) Absolute Value Inequalities
y > 2|x |

2) Absolute Value Inequalities
y > 2|x |

2) Absolute Value Inequalities
y > 2|x |

2) Absolute Value Inequalities
Example 3: Write an equation for the graph below.

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