Question

complete the table
x + 12 = 6y
x -12 -6 0 6 12
y

Answer 1

To complete the table for the equation \( x + 12 = 6y \), we need to solve for \( y \) in terms of \( x \).

Starting with the given equation:

\[
x + 12 = 6y
\]

We can rearrange it to solve for \( y \):

\[
y = \frac{x + 12}{6}
\]

Now, we can calculate \( y \) for each value of \( x \) in the table:

1. For \( x = -12 \):
\[
y = \frac{-12 + 12}{6} = \frac{0}{6} = 0
\]
2. For \( x = -6 \):
\[
y = \frac{-6 + 12}{6} = \frac{6}{6} = 1
\]
3. For \( x = 0 \):
\[
y = \frac{0 + 12}{6} = \frac{12}{6} = 2
\]
4. For \( x = 6 \):
\[
y = \frac{6 + 12}{6} = \frac{18}{6} = 3
\]
5. For \( x = 12 \):
\[
y = \frac{12 + 12}{6} = \frac{24}{6} = 4
\]

Now, we can summarize the completed table:

| \( x \) | \( y \) |
|:---------:|:-------:|
| -12 | 0 |
| -6 | 1 |
| 0 | 2 |
| 6 | 3 |
| 12 | 4 |

This is the completed table based on the equation \( x + 12 = 6y \).