IM 6.7.9 Practice: Solutions of Inequalities
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① This example demonstrates how to graph the solution set of a linear inequality on the coordinate plane and uses a slider to animate the movement of the boundary line. ② Core mathematical concepts include inequality solution sets, graphs of linear functions, and half‑plane determination in coordinate geometry. ③ Construction highlights: the `Inequality` command creates the shaded region, `Line`/`Segment` draw the boundary, a `Slider` varies the coefficients, and `ShowLabel` marks key points. ④ Suitable for middle‑school (grades 7‑9) algebra‑geometry integration lessons and for high‑school review of graphical inequality methods.
AI Drawing Prompt Reference
Create a coordinate-plane graph of the solution set of a linear inequality. Draw the boundary line for the corresponding equality case, and shade the half-plane on the side that represents the inequality’s solution region. Add a slider to vary the line’s coefficients or position so the boundary line moves as you slide, with the shaded region updating accordingly. Include a few key points or labels to highlight how the solution set relates to the boundary line and half-plane, suitable for a middle-school algebra and coordinate-geometry lesson.
The prompt above was compiled from the original drawing commands and is for reference only.