Math Example--Inequalities-- Linear Inequalities: Example 6

Topic

Inequalities

Description

This example illustrates the graphing of the linear inequality y < 6. The graph features a horizontal dashed line at y = 6, with the region below this line shaded to represent the solution set of the inequality. Quadrants III and IV are entirely shaded, demonstrating where the inequality holds true.

Linear inequalities are a fundamental concept in algebra, building upon students' understanding of linear equations and expanding it 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 grasp how different inequality symbols and equations translate into graphical form.

The importance of multiple worked-out examples cannot be overstated in helping students fully comprehend linear inequalities. Each example in this set highlights a different aspect of inequalities, allowing students to recognize patterns and develop a thorough understanding of how to graph and interpret these mathematical relationships.

Teacher's Script: Now, let's examine the inequality y < 6. Notice how this creates a horizontal line on our graph, similar to Example 3, but with a different y-value. We shade below the line because the inequality symbol is "less than." The dashed line indicates that points on y = 6 are not part of our solution. How does this example compare to the previous horizontal line inequality we saw?

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