Question

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

x	5	10	15	20
y	2	3	4	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 \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Select two points from the table

Let's choose the points \((5, 2)\) and \((10, 3)\) (we could also choose other pairs like \((10, 3)\) and \((15, 4)\), etc.).

Step3: Calculate the rate of change

Using the formula, substitute \(x_1 = 5\), \(y_1 = 2\), \(x_2 = 10\), \(y_2 = 3\).

$$ \frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 2}{10 - 5}=\frac{1}{5} $$

Let's verify with another pair, say \((10, 3)\) and \((15, 4)\):

$$ \frac{4 - 3}{15 - 10}=\frac{1}{5} $$

And with \((15, 4)\) and \((20, 5)\):

$$ \frac{5 - 4}{20 - 15}=\frac{1}{5} $$

All pairs give the same rate of change.

Answer:

The rate of change of the function is \(\frac{1}{5}\)