Answer:
The relation between x and y is
[tex]y=\frac13 x^2[/tex]
Step-by-step explanation:
Given that,
The value of y varies directly as the square of x.
[tex]y\propto x^2[/tex]
[tex]\Rightarrow y=rx^2[/tex]
where r is constant of proportional.
Given that,
y= 27 and x=9
Plug y= 27 and x=9 in above relation
[tex]y=rx^2[/tex]
[tex]\therefore 27=r(9)^2[/tex]
[tex]\Rightarrow 27 = r.81[/tex]
[tex]\Rightarrow r=\frac{27}{81}[/tex]
[tex]\Rightarrow r=\frac{1}{3}[/tex]
The relation between x and y is
[tex]y=\frac13 x^2[/tex]
