Observe the tooth

(a) Let us observe the pattern given and complete the table.

Pattern and toothpicks are related as follows

1→ 4,

2→ 4 + 3 = 7

3→ 7 + 3 = 10

4→ 10 + 3 = 13

5→ 13 + 3 = 16

6→ 16 + 3 = 19

∴ fill the above details in the table. we get,

(b) The graph is plotted as the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis.

(c) The graph follows y = 3x + 1 pattern.

If x = 7 then y = (3 ×7) + 1 = 22

If x = 8 then y = (3 ×8) + 1 = 25

(d) Yes, X and Y follows the y = 3x + 1 pattern.