Math Example--Inequalities-- Linear Inequalities: Example 9

Topic

Inequalities

Description

This example demonstrates the graphing of the linear inequality y ≥ 2. The graph shows a solid horizontal line at y = 2, with the region above this line shaded to represent the solution set of the inequality. The use of a solid line indicates that points on the line itself are included in the solution.

Linear inequalities are a crucial concept in algebra, extending students' understanding of linear equations to include regions of the coordinate plane. This collection of examples aids in teaching this topic by providing visual representations of various inequalities, helping students understand how different inequality symbols and equations translate into graphical form.

Exposure to multiple worked-out examples is essential for students to fully grasp the concept of linear inequalities. Each example in this set highlights a different aspect of inequalities, allowing students to recognize patterns and develop a comprehensive understanding of how to graph and interpret these mathematical relationships.

Teacher's Script: Let's examine the inequality y ≥ 2. Notice how this creates a horizontal line on our graph, similar to previous examples, but with a different y-value and inequality symbol. We shade above the line because the inequality symbol is "greater than or equal to." The solid line shows that points on y = 2 are part of our solution. How does this example compare to the previous horizontal line inequalities we've seen?

For a complete collection of math examples related to Inequalities click on this link: Math Examples: Inequalities Collection.