Question

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

x	y
5	9
8	15
11	21

Explanation:

Step1: Recall rate of change formula

For a linear function, rate of change (slope) is given by $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Select two points

Take the first two points: $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(5,9)$.

Step3: Calculate $\Delta y$ and $\Delta x$

$\Delta y = 9 - 3 = 6$, $\Delta x = 5 - 2 = 3$.

Step4: Compute rate of change

Rate of change $=\frac{6}{3}=2$. We can verify with other points (e.g., $(5,9)$ and $(8,15)$: $\frac{15 - 9}{8 - 5}=\frac{6}{3}=2$; or $(8,15)$ and $(11,21)$: $\frac{21 - 15}{11 - 8}=\frac{6}{3}=2$) to confirm.

Answer:

2