Question

which of the relationships below represents a function with lesser rate of change than the function y=5/2x+1

Answer 1

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).

`\begin{gathered} m=(-5-0)/(0-(-5)) \\ =(-5)/(5) \\ =-1 \end{gathered}`

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).

`\begin{gathered} m=(-4-2)/(0-1) \\ =(-6)/(-1) \\ =6 \end{gathered}`

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).

`\begin{gathered} m=(8-(-2))/(4-0) \\ =(10)/(4) \\ =(5)/(2) \end{gathered}`

The rate of change 5/2 is equal to 5/2 so option C is wrong.