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complete the table

x + 12 = 6y
x -12 -6 0 6 12
y

1 answer

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 \( x + 12 = 6y \).