The document explains the differences between linear inequalities and linear equations in two variables, highlighting that inequalities represent non-equivalence while equations indicate equivalence. It provides a step-by-step guide for graphing linear inequalities, which includes converting the inequality to an equation, plotting the graph with identified slope and y-intercept, determining the type of line (solid or broken), and shading the appropriate solution area. Multiple examples and repetition emphasize the consistent approach needed for graphing linear inequalities.

1. Differentiates Linear
Inequalities in Two
Variables From Linear
Equations in Two
Variables

2. INEQUALITIES vs EQUATION
• Inequality is a mathematical statement
where one expression is not equal to
another while Equation indicates the value
of both mathematical expressions are equal

3. FORM
Linear equation Linear Inequality

4. CHARACTERISTIC OF A GRAPH
Linear equation Linear Inequality
Straight line Plane or Half plane

5. SAMPLE GRAPH
Linear equation Linear Inequality

6. Graphical Solutions
Linear equation Linear Inequality
Set of Points Region of points bounded
by a line

7. Graphing Linear Inequalities

8. Example:
• Convert the inequality to an equation
• Identify the slope and y-intercept and plot
• Identify the type of line you will be using
Types of line
Broken line - ,
Solid line - ,
• Substitute a test point to find the solution (0, 0)
• Shade the area of the solution

9. Example:
• Convert the inequality to an equation
• Identify the slope and y-intercept and plot
• Identify the type of line you will be using
Types of line
Broken line - ,
Solid line - ,
• Substitute a test point to find the solution (0, 0)
• Shade the area of the solution

10. Example:
• Convert the inequality to an equation
• Identify the slope and y-intercept and plot
• Identify the type of line you will be using
Types of line
Broken line - ,
Solid line - ,
• Substitute a test point to find the solution (0, 0)
• Shade the area of the solution

11. Example:
• Convert the inequality to an equation
• Identify the slope and y-intercept and plot
• Identify the type of line you will be using
Types of line
Broken line - ,
Solid line - ,
• Substitute a test point to find the solution (0, 0)
• Shade the area of the solution

12. Example:
• Convert the inequality to an equation
• Identify the slope and y-intercept
• Identify the type of line you will be using
Types of line
Broken line - ,
Solid line - ,
• Substitute a test point to find the solution
• Shade the area of the solution

13. Example:
• Convert the inequality to an equation
• Identify the slope and y-intercept
• Identify the type of line you will be using
Types of line
Broken line - ,
Solid line - ,
• Substitute a test point to find the solution
• Shade the area of the solution

14. Example:
• Convert the inequality to an equation
• Identify the slope and y-intercept
• Identify the type of line you will be using
Types of line
Broken line - ,
Solid line - ,
• Substitute a test point to find the solution
• Shade the area of the solution