Tabulate and find the relationship between the variables (x and y) for

Tabulate and find the relationship between the variables (x and y) for the following patterns.

Answer»

(i) Let the number of steps be x and the number of shapes be y.

Tabulating the values of x and y

Steps(x)	1	2	3	4
Steps(y)	1	4	9	16

From the table

x = 1 ⇒ y = 1 = 12

x = 2 ⇒ y = 4 = 22

x = 3 ⇒ y = 9 = 32

x = 4 ⇒ y = 16 = 42

Hence the relationship between x and y is y = x².

(ii) Let the number of steps be x and the number of shapes be y.

Tabulating the values of x and y

Steps(x)	1	2	3	4	5
Steps(y)	1	3	5	7	9

From the table

x = 1 ⇒ y = 1 = 1

x = 2 ⇒ y = 2 + 1 = 3

x = 3 ⇒ y = 3 + 2 = 5

x = 4 ⇒ y = 4 + 3 = 7

x = 5 ⇒ y = 5 + 4 = 9

Hence the relationship between x and y is y = 2x - 1.

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