Question

Which relationship has a greater rate of change? How much

Answer 1

Let's find the rate of change of each case.

We have to use the following formula

$m=\frac{y_2-y_1_{}}{x_2-x_1}$

For function a, let's replace the points (0,0) and (5, 50), where

$\begin{gathered} x_1=0 \\ x_2=5 \\ y_1=0 \\ y_2=50 \end{gathered}$$m=\frac{50-0}{5-0}=\frac{50}{5}=10$

The rate of change for function a is 10.

Let's find the rate of change for function b using the points (3,33) and (5,55) where

$\begin{gathered} x_1=3_{} \\ x_2=5 \\ y_1=33 \\ y_2=55 \end{gathered}$$m=\frac{55-33}{5-3}=\frac{22}{2}=11$

As you can observe, function b has a greater rate of change by 1 unit.