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Linear Equations & Inequalities Example

Linear Equations & Inequalities Example
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2017-08-06 21:38
Coordinate GeometryInequalityGeometric Construction
This example demonstrates the representation and solution of linear equations and inequalities in the coordinate system. Key math concepts include linear equations, inequalities, unit circle, rational numbers, circumcircle, etc. GeoGebra commands and objects like LaTeX, Corner, Simplify, If, gb, ga, fa, solx, soly are utilized in the construction. Suitable for high school mathematics teaching to help students understand the geometric meaning and solution methods of linear equations and inequalities.

GeoGebra Commands & Parameters

  1. LaTeX(steps) → counter
  2. LaTeX("\text{Move the slider to solve the problem.}") → text0
  3. LaTeX("\text{Use the buttons below to return to the original}\cr\text{problem or randomly generate a similar practice}\cr\text{problem.}") → RandomizationText
  4. Corner(2, 3) → topright
  5. Corner(2, 1) → bottomleft
  6. Simplify((ga * x) + gb) → g
  7. LaTeX((((("\text{Graph }\textcolor{#000099}{f(x) = " * f) * "}\text{ and }\textcolor{#000099}{g(x) = ") * g) * "}\text{ on the same}\cr\text{coordinate axes.}")) → text1
  8. LaTeX((((("\text{Use a graph to approximate the solution set for the}\cr\text{following system of equations.}\cr\text{Find }\textcolor{#000099}{f(x) – g(x)}\text{ for your estimates.}\cr\textcolor{#000099}{f(x)=" * f) * "}\cr\textcolor{#000099}{g(x)=") * g) * "}")) → Problem
  9. LaTeX("\text{Approximate the values for }\textcolor{#000099}{x}\text{ where }\textcolor{#000099}{f(x) = g(x)}\text{.}") → text2
  10. LaTeX((("\text{The graphs intersect in one point. From the graph, }\cr\textcolor{#000099}{x = " * solx) * "}\text{ appears to be a good estimate.}")) → text3
  11. LaTeX((((((("\text{Evaluate }\textcolor{#000099}{f(x)=" * f) * "}\text{ and }\textcolor{#000099}{g(x)=") * g) * "}\text{ for }\textcolor{#000099}{x=") * solx) * "}.")) → text4
  12. LaTeX((("\text{Change ``}\textcolor{#000099}{f(x) =}\text{'' and ``}\textcolor{#000099}{g(x) =}\text{'' to ``}\textcolor{#000099}{y =}\text{'' and}\cr\text{substitute }\textcolor{#000099}{" * solx) * "}\text{ for }\textcolor{#000099}{x}.")) → text5
  13. LaTeX((((((((("\textcolor{#000099}{y=" * f) * "=") * fa) * "(") * solx) * ")=") * soly) * "}")) → text6
  14. If(gb > 0, LaTeX[("+" * gb)], LaTeX[gb]) → gadd
  15. LaTeX("\text{Find the difference in the y-values for the equations.}") → text8
  16. LaTeX((((((((((("\textcolor{#000099}{y=" * g) * "=") * ga) * "(") * solx) * ")") * gadd) * "=") * solyg) * "}")) → text7
  17. If(ydiff ≟ 0, LaTeX["satisfies"], LaTeX["approximately satisfies"]) → sat
  18. If(ydiff ≟ 0, LaTeX["x-coordinate"], LaTeX["approximate x-coordinate"]) → coord
  19. If(ydiff ≟ 0, LaTeX["solution"], LaTeX["approximate solution"]) → soln
  20. LaTeX((((((("\text{The point whose ordered pair is }\textcolor{#000099}{(" * solx) * ", ") * soly) * ")}\text{ is the}\cr\text{") * soln) * " of this system.}")) → text10
  21. LaTeX((((((((((((("\text{Because }\textcolor{#000099}{" * soly) * "-(") * solyg) * ")=") * ydiff) * "}\text{, }\textcolor{#000099}{x=") * solx) * "}\cr\text{") * sat) * " }\textcolor{#000099}{f(x)=g(x)}\text{ and is the}\cr\text{") * coord) * " of a solution to the}\cr\text{system.}")) → text9