IM 7.2.5 Practice: Two Equations for Each Relationship
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① This example is a practice activity from Illustrative Mathematics Grade 7 Unit 2 Lesson 5, demonstrating that a single mathematical relationship can be expressed by two different equations, such as y=kx and x=y/k for proportional relationships. ② Core math concepts include proportional relationships, linear equations, equivalent algebraic forms, and interpreting relationships from tables or graphs. ③ Construction highlights: based on the summary, multiple point objects (A1, B1, A2, A3, A4, A5, A6, A7, B2) are used, likely to plot data points or graph lines in a coordinate system, allowing students to visually compare the two equation forms. ④ Suitable for Grade 7 students learning about ratios and equations, and useful for teachers as an interactive demonstration or for independent practice to reinforce understanding of equivalent representations of the same relationship.
GeoGebra Commands & Parameters
10003500500751A7(x) = x1
AI Drawing Prompt Reference
Draw two coordinate systems, each with a line representing a proportional relationship. In the first system, draw the line y=kx with k set to 1. In the second system, draw the line x=y/k with k also set to 1. Make sure the x and y axes have the same range in both systems to visually compare the two representations.
The prompt above was compiled from the original drawing commands and is for reference only.