x = 2, 3, 4, 5, 6. y = 3, 5, 7, 9, 11

Question

the table shows different values for a linear function. calculate the rate of change of the function between 5 and 6.

Answer 1

To calculate the rate of change of a linear function between two points, you can use the formula:

\[ \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} \]

From the data given:

• For \(x = 5\), \(y = 9\)
• For \(x = 6\), \(y = 11\)

Here, \(x_1 = 5\), \(y_1 = 9\), \(x_2 = 6\), and \(y_2 = 11\).

Now, plug the values into the formula:

\[ \text{Rate of Change} = \frac{11 - 9}{6 - 5} = \frac{2}{1} = 2 \]

Thus, the rate of change of the function between \(x = 5\) and \(x = 6\) is \(2\).