Question

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

Answer 1

(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.