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=(50-0)/(5-0)=(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=(55-33)/(5-3)=(22)/(2)=11`

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