Use the table to answer the question. x y 2 3 3 5 4 7 5 9 6 11 The table shows different values for a linear function. Calculate the rate of change of the function between 5 and 6.(1 point) Responses 2 2 12 Start Fraction 1 over 2 End Fraction −2 negative 2 11

Answer 1

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

\[ \text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]

From the table, we have the following points:

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

Now, we can substitute these values into the formula:

\[ \Delta y = y_2 - y_1 = 11 - 9 = 2 \] \[ \Delta x = x_2 - x_1 = 6 - 5 = 1 \]

Now compute the rate of change:

\[ \text{Rate of change} = \frac{2}{1} = 2 \]

Thus, the rate of change of the function between 5 and 6 is 2.