Math Example--Inequalities-- Linear Inequalities: Example 11

Topic

Inequalities

Description

This example demonstrates the graphing of the linear inequality y ≤ -2x + 1. The graph shows a solid line representing the equation y = -2x + 1, with the region below the line shaded to indicate where the inequality holds true. The solid line signifies that points on the line are included in the solution set.

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 ≤ -2x + 1. Notice how we first graph the line y = -2x + 1, then shade the region below it. The solid line indicates that points on the line are included in our solution. How does this example compare to the previous one? Can you explain why the shaded region is different despite having the same inequality symbol?

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