Construct a Line Through Two Points and Find Its Slope

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2026-02-15 00:03

In collections Coordinate Geometry

This GeoGebra example demonstrates how a line in the Cartesian plane is determined by two selected points, while its slope and related linear-equation information are updated interactively. The key math ideas include the definition of slope, using two points to compute the slope, the graphical meaning of a linear function/straight line, and the correspondence between an equation and its diagram. Construction workflow: create points A and B with Point, build the line using Line (lineAB), and compute its slope with Slope (mAB). Use Textfield for user input and validation states (e.g., inputValid/inputCurrent and validA/validB/validC), then show feedback through UI objects such as btnValidate, showhint, showanswer, showsolution, and counters like tries/countCorrect/countQuestion. If multiple problem cases are generated, use Shuffle and Element to choose random coordinates and manage case selection via caseNum and related variables. Suitable for middle and high school topics such as linear functions, coordinate geometry, and slope-based line construction, and for interactive practice or guided inquiry.

GeoGebra Commands & Parameters

Shuffle({1, 2, 3, 4, 5, 6, 7}) → allCaseNum, {5, 2, 1, 7, 3, 4, 6}
Shuffle(Sequence[t, t, -6, 6, 1] \ {-1, 1}) → allCompX, {-2, 2, 6, -6, 5, 0, -5, 3, 4, -3, -4}
Shuffle(Sequence[t, t, -6, 6, 1] \ {0, -1, 1}) → allCompY, {-4, 6, 3, -5, 2, 4, -6, -3, -2, 5}
Shuffle(Join[Sequence[Sequence[(j, k), j, -10, 10, 1], k, -10, 10, 1]]) → bigGrid, {(0, -7), (-7, -7), (7, 5), (-6, 7), (2, 1), (1, -2), (-3, -9), (-5, 7), (-4, 3), (-3, 6), (2, -2), (-8, 0), (5, 7), (2, 3), (-8, 1), (10, -2), (4, 8), (-9, -4), (8, -6), (6, 5), (7, -7), (5, 8), (-3, 8), (-7, 9), (-2, 2), (5, 2), (10, -7), (2, -7), (0, -5), (4, 7), (-8, 4), (-4, -10), (9, 8), (8, -9), (-10, 8), (6, 1), (-3, -5), (-7, -9), (9, 5), (-8, -5), (8, 1), (6, 7), (-3, -2), (-9, -2), (-10, 5), (-10, -5), (5, 1), (10, 5), (0, 1), (8, 2), (1, -1), (9, 1), (4, -6), (-4, 10), (-8, 3), (-8, 5), (0, 5), (10, -4), (8, -2), (-8, -9), (2, 7), (0, 9), (8, 8), (3, -8), (5, -6), (4, 5), (-9, -10), (4, -1), (0, 6), (-4, -4), (-7, 5), (-2, 10), (-9, 2), (7, 4), (2, 9), (-8, 2), (7, 10), (-3, -10), (1, 6), (8, -5), (-1, 6), (1, -9), (8, -4), (4, 2), (1, -7), (-4, 5), (9, -8), (0, -2), (10, 7), (-2, -6), (4, -8), (9, -3), (2, 6), (-6, -8), (-10, -2), (-6, 1), (1, -4), (2, 5), (-6, -5), (-3, 10), (10, 9), (7, -1), (-7, 1), (10, -5), (-10, -8), (3, 7), (-10, 6), (9, -4), (6, -8), (-4, -9), (0, -10), (9, 9), (-10, 0), (8, -8), (4, -5), (7, -8), (-7, -1), (-5, 0), (-4, 9), (1, 5), (5, -9), (7, -2), (8, 7), (1, 2), (-10, -3), (-8, 8), (-7, 0), (5, -7), (-5, -7), (4, -3), (-9, 4), (3, -7), (3, 2), (8, -10), (-2, 1), (-5, 10), (-6, 3), (1, 10), (-1, -9), (-3, -1), (6, 4), (-2, 7), (3, -10), (-1, 5), (-9, 3), (-10, 3), (-2, -3), (-1, -1), (0, 4), (-3, 9), (4, -9), (-7, -4), (-9, -1), (-8, 9), (4, -7), (10, -3), (-3, 0), (4, -10), (-4, -2), (7, 1), (0, -8), (6, -1), (8, 6), (9, -5), (2, -6), (7, 6), (-9, 5), (-10, -1), (7, -4), (4, 3), (4, 6), (-6, -4), (6, 9), (-2, 8), (-9, 1), (-3, 1), (-1, 9), (-2, 5), (5, 9), (4, 1), (5, 3), (-2, 0), (8, 0), (5, 4), (6, -2), (-8, -10), (5, -4), (-5, 8), (-9, 8), (-7, 8), (-5, -2), (-4, 8), (-2, 4), (8, 3), (8, -7), (3, -5), (0, 3), (-3, -4), (-7, 10), (5, -5), (1, 7), (-1, 10), (3, -3), (-9, -9), (9, -1), (-9, 7), (2, -1), (0, -9), (-2, 3), (-7, -2), (6, -5), (0, 10), (-6, 8), (-7, -8), (1, -6), (5, -1), (1, -8), (-1, -5), (-10, -9), (-9, 9), (6, 0), (1, -10), (-3, -6), (8, 9), (-1, 1), (10, 6), (5, -3), (-10, 9), (-5, -6), (7, 3), (-3, -3), (-2, -10), (6, -3), (-1, 0), (0, 7), (0, -6), (-4, 4), (-6, 6), (4, -2), (6, -7), (9, 7), (5, 5), (-7, 6), (-1, 2), (4, 9), (10, 4), (-7, 4), (10, 0), (-10, -6), (3, 3), (-6, 2), (-4, 6), (-6, -3), (-9, -8), (-9, 0), (6, 6), (9, 3), (-10, 1), (6, -9), (-6, 5), (-2, 9), (6, -4), (10, -9), (1, 9), (-6, -10), (-4, 2), (-10, 7), (4, -4), (-7, 7), (-3, 4), (-8, -2), (9, -2), (6, 3), (9, 10), (-7, -10), (-5, -3), (-5, 9), (1, 4), (0, 8), (0, 2), (-6, -1), (5, 6), (-1, -8), (-5, -8), (-2, -1), (-6, -7), (1, 8), (-4, -5), (5, -10), (-9, -3), (5, -2), (-5, 6), (7, -10), (7, 0), (-4, -7), (-8, -3), (-1, -6), (10, 8), (2, -8), (-6, -9), (4, 4), (-5, -5), (-10, 10), (-9, 10), (9, -10), (0, -4), (1, -3), (5, 0), (2, -10), (-6, 10), (-8, -7), (3, -2), (-3, 2), (10, 3), (7, -5), (-8, 6), (-6, 9), (-5, 3), (2, 10), (2, 8), (-3, -7), (-5, 2), (-3, 7), (7, -9), (3, 9), (-4, 0), (7, 2), (-7, -5), (-9, 6), (6, 8), (-2, -2), (6, -6), (10, 2), (8, 4), (10, -10), (5, -8), (-6, -2), (0, -1), (3, 10), (-5, 1), (3, -1), (0, -3), (-3, 3), (-7, -6), (-1, -10), (8, -3), (9, -9), (2, 2), (6, 2), (-1, 3), (-6, 4), (10, 10), (-8, -4), (-10, -7), (2, 4), (1, 0), (-10, -10), (2, -5), (-6, -6), (3, 6), (-1, 8), (-1, -7), (-5, -4), (-7, 2), (2, -3), (2, 0), (-2, -9), (3, -4), (-9, -6), (8, 10), (-10, -4), (-2, -5), (3, 5), (9, -6), (5, 10), (-5, 5), (-4, -8), (-6, 0), (-8, 7), (9, 4), (-2, 6), (-8, -8), (-2, -7), (7, -6), (-1, 4), (1, 3), (-10, 4), (-4, -3), (-3, -8), (3, 4), (-4, 1), (-7, -3), (-4, -6), (7, -3), (1, -5), (3, 1), (1, 1), (2, -4), (-2, -8), (-2, -4), (-3, 5), (9, -7), (6, 10), (6, -10), (-8, 10), (4, 0), (-10, 2), (-8, -1), (10, 1), (4, 10), (-7, 3), (9, 2), (3, -6), (-4, -1), (10, -8), (-8, -6), (-5, -9), (10, -6), (3, -9), (-5, -1), (7, 9), (8, 5), (-1, 7), (9, 6), (-4, 7), (3, 8), (-1, -2), (7, 8), (-1, -4), (-9, -7), (-1, -3), (3, 0), (-9, -5), (2, -9), (7, 7), (10, -1), (8, -1), (-5, 4), (0, 0), (-5, -10), (9, 0)}
Element(allCaseNum, Mod[countQuestion, Length[allCaseNum]] + 1) → caseNum
Element(allCompX, Mod[countQuestion, Length[allCompX]] + 1) → compX
Element(allCompY, Mod[countQuestion, Length[allCompY]] + 1) → compY
Element(bigGrid, Mod[countQuestion, Length[bigGrid]] + 1) → V1
Point(bigGrid) → A
Point(bigGrid) → B
Line(A, B) → lineAB
Slope(lineAB) → mAB
Textfield(inputB) → InputBoxB
Corner(5) → layoutAppSize
onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
Textfield(inputA) → InputBoxA
Textfield(inputC) → InputBoxC
Polygon(P1, Mirror[P1, yAxis], Mirror[P1, (0, 0)], Mirror[P1, xAxis]) → peep, f, g, h, i
Segment((-10.8, 0), (10.8, 0)) → fakeX
Segment((0, -10.8), (0, 10.8)) → fakeY
Vector(V1, (0, 0)) → aniVec
Translate(V1, Vector[(aniSli * aniVec)]) → V1T
Translate(V2, Vector[(aniSli * aniVec)]) → V2T
Vector((10, 0), (11.2, 0)) → arrowX
Vector((0, 10), (0, 11.2)) → arrowy
If(y(A) > y(B), (x(A), y(B)), (x(B), y(A))) → C
If(y(A) > y(B), Segment[B, B + (aniSli * (C - B))], Segment[A, A + (aniSli * (C - A))]) → horProj
If(y(A) > y(B), Segment[A, A + (aniSli * (C - A))], Segment[B, B + (aniSli * (C - B))]) → vertProj

AI Drawing Prompt Reference

Draw a line through two randomly selected points in the Cartesian plane and calculate its slope. First, plot the line connecting these two points. Then, compute and display the slope of the line. To enhance interactivity, add input boxes for users to enter the coordinates of the points, and use text fields to show validation states and feedback. Finally, include coordinate axes and a grid in the plot to clearly illustrate the positions of the line and points.

The prompt above was compiled from the original drawing commands and is for reference only.