Construct a table of values for the following equation as shown.
x=y-3 for integral values of y from -2 to 6

To construct a table of values for the equation \( x = y - 3 \), we will substitute the integral values of \( y \) from -2 to 6 into the equation and find the corresponding \( x \)-values.

Here is the table of values:

\[
\begin{array}{|c|c|}
\hline
y & x = y - 3 \\
\hline
-2 & -2 - 3 = -5 \\
-1 & -1 - 3 = -4 \\
0  & 0 - 3 = -3 \\
1  & 1 - 3 = -2 \\
2  & 2 - 3 = -1 \\
3  & 3 - 3 = 0 \\
4  & 4 - 3 = 1 \\
5  & 5 - 3 = 2 \\
6  & 6 - 3 = 3 \\
\hline
\end{array}
\]

### Table:
| \( y \) | \( x = y - 3 \) |
|--------|-----------------|
|   -2   |        -5       |
|   -1   |        -4       |
|    0   |        -3       |
|    1   |        -2       |
|    2   |        -1       |
|    3   |         0       |
|    4   |         1       |
|    5   |         2       |
|    6   |         3       |

Would you like a deeper explanation or have any further questions?

Here are five related questions you might explore:
1. How would the table change if the equation was \( x = y + 3 \)?
2. What is the geometric interpretation of the equation \( x = y - 3 \)?
3. What happens to the values of \( x \) if \( y \) takes negative non-integer values?
4. Can you find an equation where \( y \) is expressed in terms of \( x \)?
5. How would you plot this table of values on a coordinate plane?

**Tip:** When solving linear equations, always remember the slope-intercept form \( y = mx + b \), as it helps you understand the relationship between \( x \) and \( y \).

Construct a table of values for the following equation as shown. x = y - 3 for integral values of y from -2 to 6.

Construct a table of values for the linear equation x = y - 3 using integral values of y from -2 to 6. This problem introduces linear equations and demonstrates how to substitute values and create a table. Suitable for students in Grades 6-8.

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