Let's plug the values and see which couple satisfy the equation: since [tex] y = 2\cdot 3^x [/tex], if we plug the values from the first option [tex] (x,y)=(1,6) [/tex] we have
[tex] 6 = 2\cdot 3^1 = 2\cdot 3 [/tex]
which is correct.
If we plug the values from the second option [tex] (x,y)=(1,9) [/tex] we have
[tex] 9 = 2\cdot 3^1 = 2\cdot 3 [/tex]
which is not correct
If we plug the values from the third option [tex] (x,y)=(2,9) [/tex] we have
[tex] 9 = 2\cdot 3^2= 2\cdot 9 [/tex]
which is not correct
If we plug the values from the fourth option [tex] (x,y)=(2,12) [/tex] we have
[tex] 12 = 2\cdot 3^2= 2\cdot 9 [/tex]
which is not correct
So, the answer is the first one.
