Graph The Solution Set of The Following Linear Inequality Calculator

How to Use This Calculator

To graph the solution set of a linear inequality:

1. Enter the coefficients for x and y in the inequality form: ax + by < c
2. Select the inequality type (<, >, ≤, ≥)
3. Click "Calculate" to generate the graph
4. View the solution set and interpretation

The calculator will display:

• The boundary line of the inequality
• The shaded region representing the solution set
• A clear interpretation of the solution

Understanding Linear Inequalities

A linear inequality is a mathematical statement that compares two linear expressions. The general form is:

Where:

• a and b are coefficients for x and y
• c is a constant
• The inequality symbol can be <, >, ≤, or ≥

The solution set of a linear inequality is all points (x, y) that make the inequality true. Graphically, this is represented by a shaded region on one side of the boundary line.

Graphing Method

Step 1: Graph the Boundary Line

First, graph the corresponding equation by:

1. Plotting two points using the equation y = (-a/b)x + (c/b)
2. Drawing a solid line if the inequality includes equality (≤ or ≥)
3. Drawing a dashed line if the inequality is strict (< or >)

Step 2: Determine the Shaded Region

Test a point not on the line to determine which side to shade:

• For < or ≤, shade below the line
• For > or ≥, shade above the line

Worked Example

Let's solve and graph the inequality: 2x + 3y < 6

Step 1: Graph the Boundary Line

First, graph the equation 2x + 3y = 6:

1. Find two points:
   • When x = 0: y = 2 (point (0,2))
   • When y = 0: x = 3 (point (3,0))
2. Draw a dashed line through these points

Step 2: Determine the Shaded Region

Test the origin (0,0):

• 2(0) + 3(0) = 0 < 6 → True
• Shade the side of the line containing (0,0)

The solution set is all points below the dashed line.