Since f(x) varies directly with x, we can write
[tex]f(x)=k\cdot x[/tex]where k is the constant of proportionality. We know that when x=5, f(5)=70, then we have
[tex]70=k\cdot5[/tex]then, k is given as
[tex]\begin{gathered} k=\frac{70}{5} \\ k=14 \end{gathered}[/tex]Then, the equation which model the problem is
[tex]f(x)=14x[/tex]Now, we can substitute x=9 into this result. It yields,
[tex]\begin{gathered} f(9)=14(9) \\ f(9)=126 \end{gathered}[/tex]Therefore, the answer is 126
