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Review on Gradient and Y-Intercept for Linear Equations

Review on Gradient and Y-Intercept for Linear Equations
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2019-04-25 17:12
FunctionCoordinate GeometryGraphing
This example demonstrates how students recognize the gradient and y-intercept values of linear equations given in various forms such as y=mx+c, ax+by=c, ax+by+c=0. Core math concepts include linear functions, coordinate geometry, slope, and y-intercept. It is constructed using GeoGebra commands like RandomElement, Random, Expand, If, Textfield, Coefficients, Intersect, Text, GCD; key objects include counter, textanswergradient, textansweryintercept, m, c, etc. Suitable for middle school and above students reviewing linear equation basics.

GeoGebra Commands & Parameters

  1. RandomElement({0, -4, -3, -2, 1, 0, 1, 2, 3, 4, 1 / 2, 1 / 3, 1 / 4, 3 / 4, 1 / 5, 2 / 3, 1 / 5, 2 / 5, 3 / 5, 4 / 5, -1 / 2, -1 / 3, -1 / 4, -3 / 4, -1 / 5, -2 / 3, -1 / 5, -2 / 5, -3 / 5, -4 / 5}) → m
  2. Random(-6, 7) → c
  3. Expand(Simplify[(m * x) + c]) → f
  4. Random(-6, 7) → a
  5. RandomElement({1, 2, 3, 4, 5, 6}) → b
  6. Random(-7, 9) → c_1
  7. If(counter < 5, 1, If[counter < 8, 2, 3]) → type
  8. If(type ≟ 1, m, If[type ≟ 2, m_d, m_d]) → m_s
  9. If(m_s ≟ m_{ans}, true, false) → answergradientcorrect
  10. If(type ≟ 1, c, c_d) → c_s
  11. If(c_s ≟ c_{ans}, true, false) → answeryinterceptcorrect
  12. Textfield(textanswergradient) → InputBox1
  13. Textfield(textansweryintercept) → InputBox2
  14. Expand(Simplify[(m_s * x) + c_s]) → f_s
  15. Coefficients(f) → l1
  16. If(m ≟ 0, "", If[abs(m) ≟ 1, If[m > 0, "x", "-x"], If[m > 0, "" + (FractionText[abs(m)]) + "x", "-" + (FractionText[abs(m)]) + "x"]]) → textCoeffX
  17. If(c ≟ 0, "", If[m ≟ 0, If[c > 0, "" + (FractionText[abs(c)]), "-" + (FractionText[abs(c)])], If[c > 0, "+" + (FractionText[abs(c)]), "-" + (FractionText[abs(c)])]]) → textConst
  18. If(c_s ≟ 0, "", If[m_s ≟ 0, If[c_s > 0, "" + (FractionText[abs(c_s)]), "-" + (FractionText[abs(c_s)])], If[c_s > 0, "+" + (FractionText[abs(c_s)]), "-" + (FractionText[abs(c_s)])]]) → textConst_s
  19. If(m_s ≟ 0, "", If[abs(m_s) ≟ 1, If[m_s > 0, "x", "-x"], If[m_s > 0, "" + (FractionText[abs(m_s)]) + "x", "-" + (FractionText[abs(m_s)]) + "x"]]) → textCoeffX_s
  20. Intersect(f_s, yAxis) → A
  21. If(f_s(Max[Denominator[m_s], 4]) > 10, (-Max[Denominator[m_s], 4]), Max[Denominator[m_s], 4]) → x_{P}
  22. If(x(A) > x(P), Vector[P, (x(A), y(P))], Vector[A, (x(P), y(A))]) → u_{AP}
  23. If(x(P) > x(A), Vector[If[y(P) > y(A), Vector[(x(P), y(A)), P], Vector[(x(P), y(A)), P]]], Vector[If[y(P) > y(A), Vector[(x(A), y(P)), A], Vector[(x(A), y(P)), A]]]) → v_{AP}
  24. Text(If[m_s < 0, "−", ""]) → textGradientSign
  25. Text("run = " + (Length[u_{AP}])) → textRun
  26. GCD({abs(a), abs(b), abs(c_1)}) → hcf

AI Drawing Prompt Reference

Draw a linear function graph, showing its slope and y-intercept. Randomly generate slope and intercept, convert the linear equation to different forms. Plot the graph in the coordinate system, and label the horizontal and vertical components of the slope with vectors. Display the correct slope and intercept values for students to identify and input.
The prompt above was compiled from the original drawing commands and is for reference only.