Geometric Relations Between Three Integers (Lines, Slopes, Inequalities)

This GeoGebra example visualizes relationships among three integers by constructing a geometric configuration that highlights how “differences” and slope-like linear relations translate into inequality constraints. It demonstrates the connection between integer parameters and linear functions (lines in the plane), emphasizing inequalities and feasible regions. The construction focuses on generating integer values with Random, then using points A, B, and C (together with integer parameters a, b, c) to build the corresponding linear relation. It also uses intermediate computed objects (e.g., bma, amc, bmc) and multiple labeled text items (text1–text4) to present the key arithmetic relations directly on the diagram. Interactive controls (button1/button2) and show are used to update and display the geometric elements, while objects like cgb/ceb/bgc represent the visible parts of the relation (e.g., angles/regions associated with the constraints). Suitable for middle to high school students learning arithmetic relations, linear functions, and inequalities, and for classroom exploration of optimization-style constraint thinking.