Question

find the rate of change of the function by using two points from the table.

x	y
10	3
15	4
20	5

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: Choose two points from the table

Let's take the first two points: \((x_1,y_1)=(5,2)\) and \((x_2,y_2)=(10,3)\).

Step3: Substitute into the formula

\(m=\frac{3 - 2}{10 - 5}=\frac{1}{5}=0.2\). We can verify with other points, e.g., \((10,3)\) and \((15,4)\): \(m=\frac{4 - 3}{15 - 10}=\frac{1}{5}=0.2\), or \((15,4)\) and \((20,5)\): \(m=\frac{5 - 4}{20 - 15}=\frac{1}{5}=0.2\).

Answer:

\(\frac{1}{5}\) (or \(0.2\))