What is an equation that models the date below

X 1,2,3,4,5

Y 3,12,27,48,75

Ooh, a puzzle so we notice that the pairs are

(1,3)

(2,12)

(3,27)

(4,48)

(5,75)

we notice also that

1 times 3=3

2 times 6=12

3 times 9=27

4 times 12=48

5 times 15=75

the numbers go up by muliplues of 3

3,6,9,12,15

3=1 times 3

6=2 times 3

9=3 times 3

12=4 times 3

15=5 times 3

1st one is 1 times 1 times 3

2nd one is 2 times 2 times 3

3rd one is 3 times 3 times 3

4th one is 4 times 4 times 3

5th one is 5 times 5 times 3

so the equation by trial and error is

if the number is x then the equation is

x times (x times 3) or using associative propery which is a (bc) = (ab) c, the equaiton is

3x^2 which means 3 times (x^2)

so the equation is y=3x^2