https://file.aiquickdraw.com/mathbot/file/1726691830099w9pfeqbd.jpg

In the image, you are working with an "Input and Output Table" where the expression for the output (Y) is given as \( Y = -1x - 2 \). Let's calculate the output (Y) values for the corresponding inputs (X).

The rule is:  
\[ Y = -1x - 2 \]

1. For \( X = -1 \):
\[
Y = -1(-1) - 2 = 1 - 2 = -1
\]
So, \( Y = -1 \).

2. For \( X = 0 \):
\[
Y = -1(0) - 2 = 0 - 2 = -2
\]
So, \( Y = -2 \).

3. For \( X = 1 \):
\[
Y = -1(1) - 2 = -1 - 2 = -3
\]
So, \( Y = -3 \).

4. For \( X = 3 \):
\[
Y = -1(3) - 2 = -3 - 2 = -5
\]
So, \( Y = -5 \).

Now, the complete table should look like this:

| Input (X) | Output (Y)  |
|-----------|--------------|
| -1        | -1           |
| 0         | -2           |
| 1         | -3           |
| 3         | -5           |

Let me know if you need more details or have further questions!

Here are 5 related questions you might find useful:
1. How would the outputs change if the rule was \( Y = -2x - 2 \)?
2. What happens to the output when the input \( X \) is a larger positive number, like 5 or 10?
3. Can you describe the relationship between the input and output in this linear function?
4. How could you graph the points \( (-1, -1), (0, -2), (1, -3), (3, -5) \)?
5. What happens if you use a positive coefficient in the rule instead of -1?

**Tip:** Linear equations of the form \( Y = mx + b \) describe straight lines, where \( m \) is the slope and \( b \) is the y-intercept.

Complete the table of values based on the expression Y = -1x - 2 for the given inputs.

Learn how to complete an input-output table using the linear equation Y = -1x - 2. This example shows how to calculate the output values for inputs -1, 0, 1, and 3, covering key algebraic concepts of linear functions. Suitable for Grades 6-8.

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