https://file.aiquickdraw.com/mathbot/file/1725557606446osa82der.jpg

The equation provided is \( y = 2x - 9 \), and the table contains some missing values that we need to fill in. Let's analyze the table step by step.

From the image, we can see:

- One row and one column are labeled \(x\) and \(y\) respectively.
- The values \(x = 0\) and \(y = 0\) are present, and we need to calculate the corresponding missing value.

### Step-by-Step Calculation:

1. When \(x = 0\), substitute it into the equation \(y = 2x - 9\):
   \[
   y = 2(0) - 9 = -9
   \]
   So, when \(x = 0\), \(y = -9\). This is one of the missing values in the table.

2. When \(y = 0\), we need to find \(x\). Set \(y = 0\) in the equation:
   \[
   0 = 2x - 9
   \]
   Solve for \(x\):
   \[
   2x = 9 \implies x = \frac{9}{2} = 4.5
   \]
   So, when \(y = 0\), \(x = 4.5\). This is the other missing value in the table.

### Final Filled Table:
| \(x\)  | \(y\)  |
|-------|-------|
| 0     | -9    |
| 4.5   | 0     |

Would you like more details on these steps or have any questions?

Here are five related questions to extend this:
1. How can we graph the equation \(y = 2x - 9\) using the points from the table?
2. What is the slope of the equation, and how does it affect the graph?
3. Can you find another point on the line by selecting a different value of \(x\)?
4. How does changing the constant in the equation (e.g., \(y = 2x - 7\)) affect the line?
5. What happens to the values of \(x\) and \(y\) if we change the coefficient of \(x\) in the equation?

**Tip:** When solving linear equations, plug in values of \(x\) or \(y\) to find corresponding pairs, which help to form the full line when plotted.

Fill in the missing parts of the table for the equation y = 2x - 9.

Learn how to solve the linear equation y = 2x - 9 by filling in the missing values in a table. This problem covers algebraic concepts related to linear equations and functions. Suitable for students in Grades 6-8.

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