Open Middle: Graphing Linear Inequalities (1)

This GeoGebra example is an interactive open-middle exercise designed for students to explore the graphical representation of linear inequalities. It demonstrates how inequalities of the form ax+by>c or ax+by≤c are plotted as half-planes on the coordinate plane, with attention to whether the boundary line is solid or dashed and which side is shaded. The core mathematical concepts include linear inequalities, half-planes, boundary lines, feasible regions, and the effect of inequality symbols on the solution set. In terms of construction, the summary reveals the use of commands such as Textfield, Mode, and If, along with multiple input boxes (InputBox1 through InputBox10) and variables a, b, c, etc., allowing dynamic adjustment of coefficients and constants. A button (button1) and various text objects (text1, text2, etc.) are included, likely for checking answers or providing feedback. This resource is suitable for middle or high school algebra and geometry classes, serving as a classroom exploration or homework task to help students understand graphing linear inequalities through hands-on manipulation and develop mathematical reasoning from concrete examples to abstract rules.