Function E is a linear function with an initial value of $2$ , and a rate of change of $\frac{1}{3}$ .

Function F is a linear function. The graph of function F includes the points $\left(2,\ 8\right)$ and $\left(0,\ 2\right)$ .

Which statement is true?

A The two functions have the same initial value.

B The two functions have the same rate of change.

C The initial value in function F is greater than the initial value in function E.

D The rate of change in function E is greater than the rate of change in function F.