Question

x y 1 12 2 19 3 26 4 33 5 40 6 47 (1 point) Responses 12 12 -12 -12 7 7 17

Answer 1

It looks like you have a set of pairs of numbers, with 'x' and 'y' values, followed by a list of responses. Let's first analyze the pairs you provided:

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

To understand the relationship between \( x \) and \( y \), we can calculate the differences:

- For \( x = 1 \) to \( x = 2 \): \( 19 - 12 = 7 \)
- For \( x = 2 \) to \( x = 3 \): \( 26 - 19 = 7 \)
- For \( x = 3 \) to \( x = 4 \): \( 33 - 26 = 7 \)
- For \( x = 4 \) to \( x = 5 \): \( 40 - 33 = 7 \)
- For \( x = 5 \) to \( x = 6 \): \( 47 - 40 = 7 \)

It seems that as \( x \) increases by 1, \( y \) increases by 7. This suggests a linear relationship.

We can express this relationship with a linear equation in the form \( y = mx + b \):

From our observations:
- The slope \( m = 7 \)
- To find \( b \), we can use one of the existing pairs. Let's use the point (1, 12):

\[ 12 = 7(1) + b \]
\[ 12 = 7 + b \]
\[ b = 5 \]

So, the equation relating \( y \) and \( x \) is:

\[ y = 7x + 5 \]

Now, let's check the responses you provided: 12, 12, -12, -12, 7, 7, 17.

It seems like you're asking which of these responses could be \( y \) values for some \( x \) values defined by the equation \( y = 7x + 5 \). Let's calculate \( y \) for different values of \( x \):

- For \( x = 0: y = 7(0) + 5 = 5 \)
- For \( x = 1: y = 7(1) + 5 = 12 \)
- For \( x = 2: y = 7(2) + 5 = 19 \)
- For \( x = 3: y = 7(3) + 5 = 26 \)
- For \( x = 4: y = 7(4) + 5 = 33 \)
- For \( x = 5: y = 7(5) + 5 = 40 \)
- For \( x = 6: y = 7(6) + 5 = 47 \)

Looking at your responses, 12 and 19 are values we found that correspond to \( y \) values for specific \( x \) values.

- The value **12** corresponds to \( x = 1 \).
- The value **19** corresponds to \( x = 2 \).

The responses **-12**, **-12**, **7**, **7**, and **17** do not match any values generated from the equation \( y = 7x + 5 \) for \( x \) values we considered.

Thus, the responses **12** and **19** are correct based on the linear relationship established, while the others do not fit.