Question

find the rate of change represented by the data in the table below. \\(\

$$\begin{array}{c|ccccc}x & 0 & 2 & 4 & 6 & 8 \\\\ \\hline y & 4 & 3 & 2 & 1 & 0\\end{array}$$

\\)

Explanation:

Step1: Recall rate of change formula

The rate of change between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Pick two data points

Choose $(x_1,y_1)=(0,4)$ and $(x_2,y_2)=(2,3)$.

Step3: Calculate rate of change

$\frac{3 - 4}{2 - 0} = \frac{-1}{2}$

Step4: Verify with another pair

Use $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(4,2)$:
$\frac{2 - 3}{4 - 2} = \frac{-1}{2}$

Answer:

$\boldsymbol{-\frac{1}{2}}$