https://file.aiquickdraw.com/mathbot/file/1726071262532q33vmgis.jpg

The image shows a table where the relationship between \(x\) and \(y\) is given by the equation:

\[
y = x + 1
\]

We need to fill in the values of \(y\) for each corresponding \(x\) value in the table.

### Calculations

1. For \(x = 4\):
   \[
   y = 4 + 1 = 5
   \]

2. For \(x = 5\):
   \[
   y = 5 + 1 = 6
   \]

3. For \(x = 6\):
   \[
   y = 6 + 1 = 7
   \]

4. For \(x = 7\):
   \[
   y = 7 + 1 = 8
   \]

### Filled Table

| \(x\) | \(y\) |
|------|-------|
| 4    | 5     |
| 5    | 6     |
| 6    | 7     |
| 7    | 8     |

The values of \(y\) corresponding to \(x = 4, 5, 6,\) and \(7\) are \(5, 6, 7,\) and \(8\), respectively.

Would you like more details or have any questions?

### Related Questions:
1. What is the slope of the equation \(y = x + 1\)?
2. How do you graph the equation \(y = x + 1\) on a coordinate plane?
3. What happens to the value of \(y\) if \(x\) is negative?
4. How can you determine if two lines are parallel?
5. How would you write the equation if it passes through a different point, such as \( (2, 5) \)?

### Tip:
When given a linear equation in the form \(y = mx + b\), \(m\) represents the slope of the line and \(b\) is the y-intercept where the line crosses the y-axis.

Given the equation y = x + 1, find the values of y for the corresponding x values: 4, 5, 6, 7.

Learn how to solve the linear equation y = x + 1 by calculating the y values for x = 4, 5, 6, and 7. This problem covers key algebraic concepts suitable for students in Grades 6-8.

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