Question

What is the rate of change of the table below?

x y
1 12
2 19
3 26
4 33
5 40
6 47


(1 point)
Responses

-12
-12

1/7
1 seventh

7
7

12

Answer 1

To find the rate of change between the values of \(y\) as \(x\) changes, we can calculate the change in \(y\) divided by the change in \(x\).

From the data:

When \(x = 1\), \(y = 12\)
When \(x = 6\), \(y = 47\)

Now, we can calculate the overall change in \(y\) and the change in \(x\):
\[
\Delta y = y_2 - y_1 = 47 - 12 = 35
\]
\[
\Delta x = x_2 - x_1 = 6 - 1 = 5
\]

Now, the rate of change (slope) is:
\[
\text{Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{35}{5} = 7
\]

Thus, the rate of change of the table is \(7\).

The correct response is:
**7**