Question 1175147

the average rate of change of {{{f(x) }}}over an interval [{{{a}}},{{{b}}}] is the slope of the 
secant line connecting the 2 points ({{{a}}},{{{f(a)}}})  and ({{{b}}},{{{f(b)}}})

average rate of change ={{{(f(b)-f(a))/(b-a)}}}

 given:

{{{x = 4 }}}and {{{x = 8}}} for the function: {{{f(x) = 12 + (4/5)x}}}

first find point ({{{a}}},{{{f(a)}}}) if{{{ a=x=4}}}

{{{f(4) = 12 + (4/5)4=76/5}}} => ({{{4}}},{{{76/5}}}) 

find point ({{{b}}},{{{f(b)}}}) if {{{a=x=8}}}

{{{f(8) = 12 + (4/5)8=92/5 }}}=> ({{{8}}},{{{92/5}}})

average rate of change ={{{(92/5-76/5)/(8-4)=(16/5)/4=4/5}}}

so, average rate of change is {{{4/5}}}