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A first quadrant graph, x axis labeled, Figure Number, scaled in ones, from 0 to 4. Y axis labeled, Number of Tiles, scaled in fives, from 0 to 30. 3 lines as follows: Line A: starts at the origin and rises slowly. Line B: starts at the point, (0, comma 30), and goes through the point, (2, comma 20). Line C, starts at the origin, and rises quickly, going through the point, ( 2, comma 20).Examine the graph at right, which displays three tile patterns.  

  1. What do you know about Figure 0 for each of the three patterns?

    What is the starting point for each pattern?

    Figure has
    Pattern A: tiles
    Pattern B: tiles
    Pattern C: tiles

  2. Which pattern changes most quickly? How quickly does it change? Show how you know.

    Find the growth of each pattern. For the pattern that changes the most quickly, the growth will be the greatest.

    Pattern C grows the most quickly at tiles per figure. Its line is the steepest.

  3. Which figure number has the same number of tiles in patterns B and C? Explain how you know.

    Where two lines on the graph intersect, the number of tiles and the figure number are the same for those two patterns.

  4. Write a rule for pattern B.

    Use the starting point for pattern B you found in part (a) and the growth you found for pattern B in part (b).