Question

current skill $ what is the rate of change? x y 2 8 3 12 4 16

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Take first two points

Let \((x_1, y_1)=(2, 8)\) and \((x_2, y_2)=(3, 12)\). Then \(m=\frac{12 - 8}{3 - 2}=\frac{4}{1} = 4\).

Step3: Verify with other points

Take \((x_2, y_2)=(3, 12)\) and \((x_3, y_3)=(4, 16)\). Then \(m=\frac{16 - 12}{4 - 3}=\frac{4}{1}=4\). The rate of change is consistent.

Answer:

4