MathPlotAI Logo MathPlotAI

Graphing Linear Relations from Intercepts

Graphing Linear Relations from Intercepts
Loading the math board and drawing, please wait…
2018-11-30 22:27
FunctionCoordinate GeometryGraphing
This example demonstrates how to graph a line using intercepts. Key mathematical concepts include linear equations. Mainly uses GeoGebra commands such as Sequence, Polygon, Element, Zip, UnicodeToLetter, DynamicCoordinates, LaTeX, FitPoly, Textfield, Line, TableText, etc. Suitable for middle school and above students to learn how to graph linear relations.

GeoGebra Commands & Parameters

  1. Sequence((i, -2.65), i, 11.5, 12.5, 1) → homeBasePoints
  2. Polygon((-7, -7), (-7, 7), (7, 7), (7, -7)) → viewBox, f, g, h, i
  3. Element(questionList, questionListIndex) → questionNum
  4. Element(B2:B5, questionNum) → currentYIntercept
  5. Element(A2:A5, questionNum) → currentXIntercept
  6. Element(C2:C5, questionNum) → dottedCorrectLine
  7. Zip(A ≟ B, A, usersPreTaskValues, B, {currentXIntercept, currentYIntercept}) → arePreTasksCorrect
  8. UnicodeToLetter(10007) → xmark
  9. UnicodeToLetter(10003) → cmark
  10. DynamicCoordinates(freeA, If[IsInRegion[freeA, viewBox], x(freeA), x(Element[homeBasePoints, 1])], If[IsInRegion[freeA, viewBox], y(freeA), y(Element[homeBasePoints, 1])]) → A
  11. DynamicCoordinates(freeB, If[IsInRegion[freeB, viewBox], x(freeB), x(Element[homeBasePoints, 2])], If[IsInRegion[freeB, viewBox], y(freeB), y(Element[homeBasePoints, 2])]) → B
  12. LaTeX("\text{Points:}") → pointsLabel
  13. LaTeX("\text{Please plot all points.}") → feedbackPlotAllPoints
  14. FitPoly(usersPoints, 1) → usersLine
  15. Element(D2:D5, questionNum) → displayEquation
  16. Textfield(textPreTask1) → ansBoxPreTask1
  17. Textfield(textPreTask2) → ansBoxPreTask2
  18. Zip("\vphantom{\dfrac{\dfrac{1}{2}}{\frac{3}{4}}}" + (If[¬A, B, ""]), A, arePreTasksCorrect, B, {("x\text{-intercept}=" * currentXIntercept), ("y\text{-intercept}=" * currentYIntercept)}) → hints
  19. Line((A2, 0), (0, B2)) → C2
  20. Line((A3, 0), (0, B3)) → C3
  21. Line((A4, 0), (0, B4)) → C4
  22. Line((A5, 0), (0, B5)) → C5
  23. TableText({hints}, "v") → preTaskLabelHint
  24. LaTeX("\text{To find the \(x\)-intercept, substitute\\\(y=0\) into \(" + displayEquation + "\) and solve for \(x\).\\To find the \(y\)-intercept, substitute\\\(x=0\) into \(" + displayEquation + "\) and solve for \(y\).}") → feedbackPreTask
  25. LaTeX("\text{\textbf{Question: }Graph the linear relation by \textbf{first} calculating the \(x\)- and \(y\)-intercepts.\\\textbf{Instructions: }Determine the intercepts. Then plot the intercepts by dragging points onto\\the grid.}") → TEXT
  26. TableText({{"\cellcolor{#ffcc80}{x\text{-intercept value}}"}, {"\vphantom{\tfrac{1}{2}}" + currentXIntercept}, {"\cellcolor{#ffcc80}{y\text{-intercept value}}"}, {"\vphantom{\tfrac{1}{2}}" + currentYIntercept}}, "|_c") → preTaskLabel

AI Drawing Prompt Reference

Draw a line by first finding its x-intercept and y-intercept. The x-intercept is where the line crosses the x-axis when y=0, and the y-intercept is where the line crosses the y-axis when x=0. Use the given x-intercept and y-intercept values to place points on the grid, then draw the line connecting these two points.
The prompt above was compiled from the original drawing commands and is for reference only.