The average rate of change from x = a to x = b is:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]In this question:
a = 0
b = 8
So, let's find f(a) = f(0):
[tex]\begin{gathered} f(x)=\frac{2x-2}{5x-6} \\ f(0)=\frac{2*0-2}{5*0-6} \\ f(0)=\frac{-2}{-6}=\frac{1}{3} \end{gathered}[/tex]Now, let's find f(b) = f(8):
[tex]\begin{gathered} f(8)=\frac{2*8-2}{5*8-6} \\ f(8)=\frac{16-2}{40-6} \\ f(8)=\frac{14}{34} \\ f(8)=\frac{7}{17} \end{gathered}[/tex]Substituting the values in the first equation:
[tex]\begin{gathered} \frac{f(b)-f(a)}{b-a} \\ \frac{f(8)-f(a)}{8-0} \\ \frac{\frac{7}{17}-\frac{1}{3}}{8} \\ \frac{\frac{21-17}{17*3}}{8} \\ \frac{\frac{4}{51}}{8}=\frac{4}{51}*\frac{1}{8} \\ =\frac{1}{102} \end{gathered}[/tex]Answer: 1/102.