Math Example--Inequalities-- Linear Inequalities: Example 5

Topic

Inequalities

Description

This example demonstrates the graphing of the linear inequality y < -3x + 4. The graph shows a dashed line representing the equation y = -3x + 4, with the region below the line shaded to indicate where the inequality holds true. Quadrants II and III are predominantly shaded, illustrating the solution set of this inequality.

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 look at the inequality y < -3x + 4. Notice how we first graph the line y = -3x + 4, then shade the region below it. The dashed line shows that points on the line are not part of our solution. Can you explain why Quadrants II and III are mostly shaded in this example?

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