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Linear Inequality Modeling for Streaming Service Costs

Linear Inequality Modeling for Streaming Service Costs
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2015-09-26 00:04
FunctionInequalitySlider AnimationGraphing
In collections CCSS Support Algebra I Unit 1
This example demonstrates the linear inequality phenomenon of accumulating video streaming monthly fees and setup costs. Core concepts involve linear function modeling and solving one-variable linear inequalities. Construction utilizes GeoGebra sliders to control variables, text objects to display calculation steps, and line objects to build the cost model. Suitable for middle and high school algebra teaching, helping students intuitively understand inequality applications in real life.

GeoGebra Commands & Parameters

  1. LaTeX("\text{Solve the inequality for the unknown variable.}") → text21
  2. LaTeX("\text{Write an inequality to represent the situation.}") → text8
  3. LaTeX("\text{Inequality from the previous step}") → text24
  4. LaTeX("\text{Simplify.}") → text29
  5. Line(A, B) → a_1
  6. LaTeX("\text{one term of the inequality.}") → text13
  7. LaTeX("\text{}") → text19
  8. LaTeX("\text{The total amount Cory has paid so far is the sum of the monthly rate and the one-time fee, }") → text15
  9. LaTeX((((("\text{The one-time fee is \textcolor{#000099}{" * b) * "}, so this value is represented by a constant:\textcolor{#000099}{") * b) * "}.}")) → text14
  10. LaTeX((((((((("\text{\textcolor{#000099}{" * c) * "}, write \textcolor{#000099}{") * a) * " m + ") * b) * "} on the left side of the less than symbol and \textcolor{#000099}{") * c) * "} on the right side of the symbol.}")) → text18
  11. LaTeX((((((("\text{ \textcolor{#000099}{" * a) * "m + ") * b) * " < ") * c) * "}}")) → text22
  12. LaTeX((("\text{Subtract \textcolor{#000099}{" * b) * "} from both sides.}")) → text25
  13. LaTeX((("\text{Divide both sides by \textcolor{#000099}{" * a) * "}.}")) → text26
  14. LaTeX((((("\text{ \textcolor{#000099}{" * a) * " m < ") * cb) * "}}")) → text23
  15. LaTeX((("\text{Cory could have been using the service for any number of months less than \textcolor{#000099}{" * s) * "}.}")) → text30
  16. Expand(((2 * x) * ((3 * x) - y))) → d
  17. LaTeX((((((((("\text{\textcolor{#000099}{\frac{" * a) * " m}{") * a) * "}< \frac{") * cb) * "}{") * a) * "}}}")) → text27
  18. LaTeX((("\text{ \textcolor{#000099}{m < " * s) * "}}")) → text28
  19. LaTeX("\text{that are not equivalent}") → text31_3
  20. LaTeX("\text{Since the problem uses the word under, use a less than symbol (\textcolor{#000099}{<}).}") → text11
  21. LaTeX("\text{Monthly rate \textendash}") → text2
  22. LaTeX((("\text{\textcolor{#000099}{" * a) * "}; One-time fee \textendash }")) → text5
  23. LaTeX("\text{Let \textcolor{#000099}{m} represent the number of months Cory has been subscribing to the service.}") → text9
  24. LaTeX((((((((("\text{so add the terms \textcolor{#000099}{" * a) * "m} and \textcolor{#000099}{") * b) * ": ") * a) * " m + ") * b) * "}.}")) → text16
  25. LaTeX((((((("\text{Therefore, the inequality is \textcolor{#000099}{" * a) * " m + ") * b) * " < ") * c) * "}.}")) → text20
  26. LaTeX((((("\text{The rate increases by \textcolor{#000099}{" * a) * "} for each month \textcolor{#000099}{m} that Cory subscribes. Therefore,\textcolor{#000099}{") * a) * "m} represents }")) → text12
  27. LaTeX((((((("\text{Cory has paid less than \textcolor{#000099}{" * c) * "} so far. Since what Cory has paid so far,\textcolor{#000099}{") * a) * "m + ") * b) * "}, is less than}")) → text17
  28. LaTeX((("\text{\textcolor{#000099}{" * c) * "}}")) → text7
  29. LaTeX((("\text{\textcolor{#000099}{" * b) * "}; Paid amount \textendash \textcolor{#000099}{under} }")) → text6
  30. LaTeX("\text{quantities are equal}") → text31_1
  31. LaTeX("\text{\mathbf{equation} a mathematical sentence that uses an equal sign (=) to show that two }") → text31
  32. LaTeX("\text{\mathbf{inequality} a mathematical sentence that shows the relationship between quantities }") → text31_2

AI Drawing Prompt Reference

Create an algebra illustration modeling a streaming service cost inequality. A coordinate graph shows a sloped linear line representing total cost versus subscription months, paired with interactive variable sliders for monthly rate a, one-time fee b, and spending cap c. Floating text panels walk through the derivation: define m as months, build am+b<c, isolate m by subtracting b then dividing by a, arriving at m<s. Include glossary cards defining equation and inequality with key symbols highlighted in blue. The visual layout guides students from real-world scenario to symbolic reasoning, using clean geometric lines, labeled sliders, and color-coded terms to reinforce the connection between graphical and algebraic representations of linear inequalities.
The prompt above was compiled from the original drawing commands and is for reference only.