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:

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.