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

-12
-12

7
7

17
1 seventh

Answer 1

To find the rate of change of the values in the table, we can calculate the difference in the \(y\) values divided by the difference in the \(x\) values between consecutive points.

Let's calculate this step-by-step:

1. From \(x = 1\) to \(x = 2\):
\[
\frac{19 - 12}{2 - 1} = \frac{7}{1} = 7
\]

2. From \(x = 2\) to \(x = 3\):
\[
\frac{26 - 19}{3 - 2} = \frac{7}{1} = 7
\]

3. From \(x = 3\) to \(x = 4\):
\[
\frac{33 - 26}{4 - 3} = \frac{7}{1} = 7
\]

4. From \(x = 4\) to \(x = 5\):
\[
\frac{40 - 33}{5 - 4} = \frac{7}{1} = 7
\]

5. From \(x = 5\) to \(x = 6\):
\[
\frac{47 - 40}{6 - 5} = \frac{7}{1} = 7
\]

The rate of change between each consecutive point is consistently \(7\).

Thus, the rate of change is:

**7**