Distance-Time Graph for Adam's Run

GeoGebra Commands & Parameters

1. SelectedIndex(Miles) → Getmiles
2. Vector(A, B) → u
3. OrthogonalLine(B, xAxis) → b
4. OrthogonalLine(B, b) → c
5. Point(c) → C
6. OrthogonalLine(C, c) → d
7. Point(xAxis) → D
8. OrthogonalLine(D, d) → e
9. Intersect(b, e) → E
10. Segment(B, C) → Toplinef
11. Segment(B, E) → Sidelineg
12. Polygon(F, G, H, I) → GCSplitpoly1, f, g, h, i
13. Polygon(J, K, L, M) → Gtoppoly1, j, k, l, m
14. Segment(N, O) → n
15. Segment(N, P) → p
16. Segment(P, Q) → q
17. Intersect(f, k) → R
18. Point(f) → S
19. Segment(R, S) → r
20. LaTeX("\text{Minutes spent running}") → XGramins
21. VerticalText("Miles traveled") → YGramil
22. LaTeX("\text{Describe the slope of the line.}") → PG1E
23. LaTeX("\text{The line increases from left to right; therefore, its slope is positive.}") → PG1F
24. LaTeX("\text{Explain what the slope of the line reveals about Adam’s running.}") → PG1I
25. LaTeX("\text{Because the slope is positive and the function increases as time passes, this means}") → PG1J
26. LaTeX("\text{that the longer Adam runs, the farther he will go.}") → PG1K
27. LaTeX("\text{Describe the domain.}") → PG2A
28. LaTeX("\text{The graph starts at the origin and continues through Quadrant I. No negative values}") → PG2C
29. LaTeX("\text{Explain why the domain is limited.}") → PG2E
30. LaTeX("\text{Note that the scale on the \textcolor{#000099}{x}-axis is in increments of \textcolor{#000099}{5} instead of \textcolor{#000099}{1}. If the scale on}") → PG1G
31. LaTeX("\text{the \textcolor{#000099}{x}-axis were the same as the scale on the \textcolor{#000099}{y}-axis, the slope would be steeper.}") → PG1H
32. LaTeX("\text{The domain is the set of all possible \textcolor{#000099}{x}-values for a function.}") → PG2B
33. LaTeX("\text{for \textcolor{#000099}{x} are shown. Thus, the domain is \textcolor{#000099}{x ≥ 0}.}") → PG2D
34. LaTeX("\text{In this situation, \textcolor{#000099}{x} represents the amount of time Adam spends running. Because}") → PG2F
35. LaTeX("\text{it is impossible to have a negative amount of time, \textcolor{#000099}{x} cannot be less than \textcolor{#000099}{0}.}") → PG2G
36. LaTeX("\text{Therefore, the domain is limited to values greater than or equal to \textcolor{#000099}{0}.}") → PG2H
37. Intersect(l, m) → A_1
38. Polygon(A_1, D_1, E_1, F_1) → Hideright, a_1, d_1, e_1, f_1
39. Point(k) → G_1
40. Point(q) → H_1
41. Segment(G_1, H_1) → s
42. Polygon(I_1, K_1, L_1, M_1) → Gtopnew, i_1, k_1, l_1, m_1
43. LaTeX((("\text{ Adam runs at an average speed of \textcolor{#000099}{" * Getmiles) * "} mph. Describe the graph’s slope and what it}")) → PG1A
44. LaTeX("\text{ reveals about Adam’s running. Then describe the domain and explain why it is limited.}") → PG1C
45. LaTeX("\text{\mathbf{slope} the measure of the rate of change of one variable with respect to another }") → text3
46. LaTeX("\text{without restriction}") → text2
47. LaTeX("\text{\mathbf{domain} the set of all input values (\textcolor{#000099}{x}-values) that satisfy the given function }") → WTK4
48. LaTeX("\text{variable;\textcolor{#000099}{slope=\frac{y₂-y₁}{x₂-x₁}=\frac{\Delta y}{\Delta x}=\frac{rise}{run}}; the slope in the equation \textcolor{#000099}{{y = mx + b}} is \textcolor{#000099}{m}.}") → text5