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:

$\begin{gathered} \text{Rate of change=}\frac{40-20}{2-1} \\ =20 \end{gathered}$

Option B

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

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

Option C

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

$\begin{gathered} \text{Rate of change=}\frac{18-12}{6-4} \\ =\frac{6}{2} \\ =3 \end{gathered}$

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.