Question

Which of the following represents the greatest rate of change?

Answer 1

Option A

Using points (1,20) and (2,40) from the graph:

`\begin{gathered} \text{Rate of change=}(40-20)/(2-1) \\ =20 \end{gathered}`

Option B

Using points (-1,6) and (1,10) on the table:

`\begin{gathered} \text{Rate of change=}(10-6)/(1-(-1)) \\ =(4)/(2) \\ =2 \end{gathered}`

Option C

We have the points (4,12) and (6,18).

`\begin{gathered} \text{Rate of change=}(18-12)/(6-4) \\ =(6)/(2) \\ =3 \end{gathered}`

Option D

Comparing y=3x+7 with the slope-intercept form:

`\begin{gathered} m=3 \\ \implies\text{Rate of change=3} \end{gathered}`

Thus, the first graph (option A) has the greatest rate of change.