Question

the table below represents a linear function. identify the rate of change of the function.

x	y
-4	4
0	-3
4	-10
8	-17

Explanation:

Step1: Recall rate of change formula

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

Step2: Select two points from table

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

Step3: Substitute into slope formula

$\frac{-3 - 4}{0 - (-4)} = \frac{-7}{4}$

Step4: Verify with another pair

Use $(x_1,y_1)=(0,-3)$ and $(x_2,y_2)=(4,-10)$:
$\frac{-10 - (-3)}{4 - 0} = \frac{-7}{4}$

Answer:

$\frac{-7}{4}$