2.7 two-variable inequalities
DESCRIPTION
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… - PowerPoint PPT PresentationTRANSCRIPT
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2.7 Two-Variable Inequalities
1. Graphing Linear Inequalities2. 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
![Page 4: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/4.jpg)
1) Graphing Linear Inequalities
• What it shows…– the values on the coordinate plane that
apply to the function
• What an equation looks like…
![Page 5: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/5.jpg)
1) Graphing Linear Inequalities
• What it shows…– the values on the coordinate plane that
apply to the function
• What an equation looks like…1) Inequality
symbol
2) Slope
3) 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 InequalitiesA 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 InequalitiesA 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
Example 1:Graph the inequality y < 2x + 2
Remember… y = mx + b
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1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 2
Remember… y = mx + b
![Page 12: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/12.jpg)
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 2
![Page 13: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/13.jpg)
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 2
![Page 14: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/14.jpg)
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 2
![Page 15: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/15.jpg)
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 2
y <
DASHED line
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1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 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 –int =
m =
inequality type
y = mx + b
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1) Graphing Linear Inequalities
Example 2:Write an inequality for the graph
below.y –int =
m =
inequality type
y = mx + b
![Page 20: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/20.jpg)
1) Graphing Linear Inequalities
Example 2:Write an inequality for the graph
below.y –int = -3
m =
inequality type
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 >
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
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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| + 3
DASHED line
Shade BELOW
slope = 1 Vertex = (2, 3)
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2) Absolute Value Inequalities
Example 1:Graph y < |x – 2| + 3
DASHED line
Shade BELOW
slope = 1 Vertex = (2, 3)
![Page 30: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/30.jpg)
2) Absolute Value Inequalities
Example 1:Graph y < |x – 2| + 3
DASHED line
Shade BELOW
slope = 1 Vertex = (2, 3)
![Page 31: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/31.jpg)
2) Absolute Value Inequalities
Example 1:Graph y < |x – 2| + 3
DASHED line
Shade BELOW
slope = 1 Vertex = (2, 3)
![Page 32: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/32.jpg)
2) Absolute Value Inequalities
Example 1:Graph y < |x – 2| + 3
DASHED line
Shade BELOW
slope = 1 Vertex = (2, 3)
![Page 33: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/33.jpg)
2) Absolute Value Inequalities
Example 1:Graph y < |x – 2| + 3
DASHED line
Shade BELOW
slope = 1 Vertex = (2, 3)
![Page 34: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/34.jpg)
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 + 2| + 1
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2) Absolute Value Inequalities
y > 2|x + 2| + 1
Vertex = (-2, 1)Slope = 2Solid line
Shade above
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2) Absolute Value Inequalities
y > 2|x + 2| + 1
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2) Absolute Value Inequalities
y > 2|x + 2| + 1
![Page 40: 2.7 Two-Variable Inequalities](https://reader036.vdocuments.net/reader036/viewer/2022062408/56813291550346895d992730/html5/thumbnails/40.jpg)
2) Absolute Value Inequalities
y > 2|x + 2| + 1
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2) Absolute Value Inequalities
y > 2|x + 2| + 1
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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, THURSDAYTest FRIDAY (Chapter 2 ONLY)
Extra-help WEDNESDAY at LUNCH