To solve this problem, we need to determine the equation that shows the relationship between $x$ and $y$. The equation is in the form:

$y = mx + b$

where $m$ is the slope of the line, and $b$ is the y-intercept.

Step 1: Determine the Slope (m)

The slope $m$ can be calculated using two points from the table. Let's use the points $(-5, 17)$ and $(-4, 14)$:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the values:

$m = \frac{14 - 17}{-4 - (-5)} = \frac{-3}{1} = -3$

So, the slope $m = -3$.

Step 2: Determine the y-intercept (b)

Now that we know $m = -3$, we can use one of the points to find the y-intercept $b$. Let's use the point $(-5, 17)$:

$y = mx + b \implies 17 = (-3)(-5) + b$

Calculating further:

$17 = 15 + b \implies b = 2$

Step 3: Form the Equation

Now we have the slope $m = -3$ and the y-intercept $b = 2$. Therefore, the equation is:

$y = -3x + 2$

Conclusion

The value that belongs in the green box is -3.

Would you like more details or have any questions?

Here are 5 questions to consider:

1. How do you determine the slope between two points?
2. Why is it important to find the y-intercept after determining the slope?
3. Can you use other points from the table to verify the equation?
4. How would the equation change if the slope were positive?
5. What happens to the graph of the line if the y-intercept is changed?

Tip: Remember, the slope tells you how much $y$ changes for each change in $x$, and the y-intercept is where the line crosses the y-axis.