average rate=(change in y)/(change in x)
if f(x)=-x/3
r=( f(2)-f(-2) )/(2--2)
r=(-2/3-2/3)/(2+2)
r=(-4/3)/4
r=-4/12
r=-1/3
For a line, this is always true, since all lines have a constant velocity, the average velocity over any interval is equal to the slope.