Math Example--Inequalities-- Linear Inequalities: Example 12

Topic

Inequalities

Description

This example illustrates the graphing of the linear inequality y ≤ -3. The graph features a solid horizontal line at y = -3, with the region below 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 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 ≤ -3. Notice how this creates a horizontal line on our graph, similar to previous examples, but with a different y-value. We shade below the line because the inequality symbol is "less than or equal to." The solid line shows that points on y = -3 are part of our solution. How does this example compare to the other horizontal line inequalities we've seen? Can you think of real-world situations where this type of inequality might be useful?

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