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2.7 Two-Variable Inequalities
1. Graphing Linear Inequalities2. 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…1) Inequality
symbol
2) Slope
3) 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 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 >
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 >
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
Remember… y = mx + b
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 2
Remember… y = mx + b
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 2
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 2
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 2
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 2
y <
DASHED line
1) Graphing Linear Inequalities
Example 1:Graph the inequality y < 2x + 2
m = 2
y-int = 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 –int =
m =
inequality type
y = mx + b
1) Graphing Linear Inequalities
Example 2:Write an inequality for the graph
below.y –int =
m =
inequality type
y = mx + b
1) Graphing Linear Inequalities
Example 2:Write an inequality for the graph
below.y –int = -3
m =
inequality type
y = mx + b
1) Graphing Linear Inequalities
Example 2:Write an inequality for the graph
below.y –int = -3
m = -3/2
inequality type >
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
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| + 3
DASHED line
Shade BELOW
slope = 1 Vertex = (2, 3)
2) Absolute Value Inequalities
Example 1:Graph y < |x – 2| + 3
DASHED line
Shade BELOW
slope = 1 Vertex = (2, 3)
2) Absolute Value Inequalities
Example 1:Graph y < |x – 2| + 3
DASHED line
Shade BELOW
slope = 1 Vertex = (2, 3)
2) Absolute Value Inequalities
Example 1:Graph y < |x – 2| + 3
DASHED line
Shade BELOW
slope = 1 Vertex = (2, 3)
2) Absolute Value Inequalities
Example 1:Graph y < |x – 2| + 3
DASHED line
Shade BELOW
slope = 1 Vertex = (2, 3)
2) Absolute Value Inequalities
Example 1:Graph y < |x – 2| + 3
DASHED line
Shade BELOW
slope = 1 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| + 1
2) Absolute Value Inequalities
y > 2|x + 2| + 1
Vertex = (-2, 1)Slope = 2Solid line
Shade above
2) Absolute Value Inequalities
y > 2|x + 2| + 1
2) Absolute Value Inequalities
y > 2|x + 2| + 1
2) Absolute Value Inequalities
y > 2|x + 2| + 1
2) Absolute Value Inequalities
y > 2|x + 2| + 1
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, THURSDAYTest FRIDAY (Chapter 2 ONLY)
Extra-help WEDNESDAY at LUNCH