Cost Function Example for Shirts

GeoGebra Commands & Parameters

1. Polygon(A, B, C, D) → Toppoly1, a, b, c, d
2. Polygon(E, F, G, H) → Rightpoly1, e, f, g, h
3. Polygon(I, J, K, L) → Topnewpoly, i, j, k, l
4. LaTeX("\text{Create a table to show how the two quantities described vary.}") → Pg1A
5. LaTeX("\text{The two quantities described are the number of shirts and the total cost of the shirts}") → Pg1B
6. LaTeX("\text{ (including shipping).}") → Pg1B1
7. LaTeX("\text{Choose several values for the number of shirts and calculate the associated cost.}") → Pg1D
8. LaTeX("\text{Graph the relationship.}") → Pg2A
9. LaTeX("\text{Use the table of values to graph the relationship.}") → Pg2B
10. LaTeX("\text{Determine the slope and what it means in the context of the problem.}") → Pg3A
11. LaTeX("\text{slope\textcolor{#000099}{ =\frac{y₂-y₁}{x₂-x₁}}}") → Pg3E
12. LaTeX("\text{Slope formula}") → Pg3E2
13. LaTeX((((("\text{slope\textcolor{#000099}{ =\frac{(" * G2) * ")-(") * G1) * ")}{(2)-(1)}}}")) → Pg3F
14. LaTeX((("\text{slope\textcolor{#000099}{ =\frac{" * SUG) * "}{1}}}")) → Pg3G
15. LaTeX("\text{Subtract.}") → Pg3G2
16. LaTeX((("\text{slope\textcolor{#000099}{ =" * SUG) * "}}")) → Pg3H
17. LaTeX("\text{Simplify.}") → Pg3H2
18. LaTeX("\text{graphed values.}") → Pg4C
19. LaTeX("\text{\textcolor{#000099}{x}-coordinate.}") → Pg4E
20. Mod(F1, CF1) → Cond
21. If(Cond ≠ 0, LaTeX["\text{number of shirts needs to be a whole number.}"]) → Pg4J
22. Vector(G0, Gtry) → Vector
23. LaTeX((("\text{Use the slope to determine how many shirts can be purchased for \textcolor{#000099}{\textdollar" * S3) * "}.}")) → Pg4A
24. LaTeX((("\text{The number of shirts that can be purchased for \textcolor{#000099}{\textdollar" * S3) * "} can be estimated from the}")) → Pg4B
25. OrthogonalLine(GF, xAxis) → m
26. OrthogonalLine(GF, yAxis) → n
27. LaTeX((((("\text{then adding \textcolor{#000099}{" * S2) * "} to include the \textcolor{#000099}{\textdollar") * S2) * "} shipping fee.}")) → Pg1C1
28. LaTeX((("\text{The total cost can be determined by multiplying the number of shirts by \textcolor{#000099}{" * S1) * "} and}")) → Pg1C
29. OrthogonalLine(DUMMY, m) → p
30. OrthogonalLine(DUMMY, p) → q
31. Intersect(n, q) → M
32. Intersect(m, p) → N
33. Segment(M, GF) → r
34. Segment(GF, N) → s
35. LaTeX((("\text{Cost of a shirt=\textdollar" * S1) * "}")) → DKT1
36. LaTeX((("\text{Standard shipping fee=\textdollar" * S2) * "}")) → DKT2
37. VerticalText("\text{Cost \textcolor{#000099}{(\textdollar)}") → VertYaxis
38. LaTeX("\text{Let \textcolor{#000099}x represent the number of shirts and \textcolor{#000099}y represent the cost in dollars.}") → Pg2C
39. LaTeX((("\text{problem that each shirt costs \textcolor{#000099}{\textdollar" * SUG) * "}.}")) → Pg3J
40. TableText({{LaTeX["\text{\mathbf{Number\;of\;shirts}}"], LaTeX[(("\text{\textcolor{#000099}{" * H1) * "}}")], LaTeX[(("\text{\textcolor{#000099}{" * H2) * "}}")], LaTeX[(("\text{\textcolor{#000099}{" * H3) * "}}")], LaTeX[(("\text{\textcolor{#000099}{" * H4) * "}}")], LaTeX[(("\text{\textcolor{#000099}{" * H5) * "}}")]}, {LaTeX["\text {\mathbf{Calculation}}"], LaTeX[(((((((("\text{\textcolor{#000099}{" * S1) * "(") * H1) * ") + ") * S2) * " = ") * G1) * " }}")], LaTeX[(((((((("\text{\textcolor{#000099}{" * S1) * "(") * H2) * ") + ") * S2) * " = ") * G2) * " }}")], LaTeX[(((((((("\text{\textcolor{#000099}{" * S1) * "(") * H3) * ") + ") * S2) * " = ") * G3) * " }}")], LaTeX[(((((((("\text{\textcolor{#000099}{" * S1) * "(") * H4) * ") + ") * S2) * " = ") * G4) * " }}")], LaTeX[(((((((("\text{\textcolor{#000099}{" * S1) * "(") * H5) * ") + ") * S2) * " = ") * G5) * "}}")]}, {LaTeX["\text{\mathbf{Cost\;(\textcolor{#000099}{\textdollar})}}"], LaTeX[(("\text{\textcolor{#000099}{" * G1) * "}}")], LaTeX[(("\text{\textcolor{#000099}{" * G2) * "}}")], LaTeX[(("\text{\textcolor{#000099}{" * G3) * "}}")], LaTeX[(("\text{\textcolor{#000099}{" * G4) * "}}")], LaTeX[(("\text{\textcolor{#000099}{" * G5) * "}}")]}}, "vc|_") → Table
41. LaTeX((("\text{How many shirts can be purchased for \textcolor{#000099}{\textdollar " * S3) * "}? Assume there is no sales tax.}")) → Question2
42. LaTeX((((("\text{Cost of a shirt:\textcolor{#000099}{\textdollar" * S1) * "}; Standard shipping fee: \textcolor{#000099}{\textdollar") * S2) * "}}")) → Question1
43. LaTeX((("\text{Determine the slope by using the slope formula, slope\textcolor{#000099}{=}\textcolor{#000099}{ \frac{y₂-y₁}{x₂-x₁}}. Let (\textcolor{#000099}{x₁,y₁}) be (\textcolor{#000099}{1},\textcolor{#000099}{" * G1) * "})}")) → Pg3B
44. LaTeX((("\text{and (\textcolor{#000099}{x₂,y₂}) be (\textcolor{#000099}{2," * G2) * "}). Substitute these values into the slope formula to find the slope}")) → Pg3C
45. LaTeX("\text{of the line, and then simplify.}") → Pg3D
46. LaTeX((((("\text{Substitute \textcolor{#000099}{" * G1) * "} for \textcolor{#000099}{y₁}, \textcolor{#000099}{") * G2) * "} for \textcolor{#000099}{y₂}, \textcolor{#000099}{1} for \textcolor{#000099}{x₁}, and \textcolor{#000099}{2} for \textcolor{#000099}{x₂}.}")) → Pg3F2
47. LaTeX((((("\text{The slope is \textcolor{#000099}{" * SUG) * "}, or \textcolor{#000099}{\textdollar") * SUG) * "} per shirt. This verifies the given information in the}")) → Pg3I
48. LaTeX((("\text{Find \textcolor{#000099}{" * S3) * "} on the \textcolor{#000099}{y}-axis, and then look to the right to determine the corresponding }")) → Pg4D
49. LaTeX((((("\text{From the graph, it appears that for \textcolor{#000099}{\textdollar" * S3) * "}, about \textcolor{#000099}{") * CF1) * "} shirts can be purchased.}")) → Pg4F
50. LaTeX((("\text{Using the rate of \textcolor{#000099}{\textdollar" * S1) * "} per shirt, the number of shirts can also be found by first subtracting}")) → Pg4G
51. LaTeX((((((((("\text{\textcolor{#000099}{" * S2) * "} from \textcolor{#000099}{") * S3) * "} and then dividing the result by \textcolor{#000099}{") * S1) * "}. This yields a result of \textcolor{#000099}{") * F1) * "};}")) → Pg4H
52. If(Cond ≠ 0, LaTeX[(((("\text{however, in the context of this problem, \textcolor{#000099}{" * F1) * "} must be rounded down to \textcolor{#000099}{") * CF1) * "}, since the}")]) → Pg4I
53. LaTeX("\text{\mathbf{slope} the measure of the rate of change of one variable with respect to another}") → WTK1
54. LaTeX("\text{variable; slope\textcolor{#000099}{ =\frac{y₂-y₁}{x₂-x₁}}\textcolor{#000099}{ =\frac{\triangle y}{\triangle x}}\textcolor{#000099}{=\frac{rise}{run}}; the slope in the equation \textcolor{#000099}{y = mx + b} is \textcolor{#000099}{m}.}") → WTK2
55. LaTeX((("\text{Total paid=\textdollar" * S3) * "}")) → DKT3