The rate of change of function y=5/2x+1 is 5/2.
Determine the rate of change for the equation drawn on option A.
The line passes through point (-5,0) and (0,-5).
[tex]\begin{gathered} m=\frac{-5-0}{0-(-5)} \\ =\frac{-5}{5} \\ =-1 \end{gathered}[/tex]The rate of change is -1 which is less than 5/2. So this option is correct.
Check for the other options.
Determine the rate of change for graph of option B.
The line passes through point (1,2) and (0,-4).
[tex]\begin{gathered} m=\frac{-4-2}{0-1} \\ =\frac{-6}{-1} \\ =6 \end{gathered}[/tex]The rate of change 6 is more than 5/2 so option B is not correct.
Consider option C.
Determine the slope of line passes through point (0,-2) and (4,8).
[tex]\begin{gathered} m=\frac{8-(-2)}{4-0} \\ =\frac{10}{4} \\ =\frac{5}{2} \end{gathered}[/tex]The rate of change 5/2 is equal to 5/2 so option C is wrong.