The table shows the relationship between $x$ and $y$, and we need to find the equation in the form $y = mx + b$. To determine the relationship, we need to identify the slope ($m$) and y-intercept ($b$).

Step 1: Identify the Slope ($m$)

The slope $m$ can be found using the formula:

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

Using the first two points from the table $(0, -6)$ and $(1, -4)$:

$m = \frac{-4 - (-6)}{1 - 0} = \frac{-4 + 6}{1} = \frac{2}{1} = 2$

Step 2: Find the y-intercept ($b$)

Since $b$ is the value of $y$ when $x = 0$, we can see directly from the table that:

$b = -6$

Step 3: Write the Equation

Substituting $m = 2$ and $b = -6$ into the equation:

$y = 2x - 6$

So, the missing number in the green box is $2$.

Would you like further details or have any questions?

Related Questions:

1. How do you find the slope if the points are not given in a table?
2. What is the significance of the y-intercept in an equation?
3. How can you verify that an equation matches all given points?
4. What are other forms of linear equations besides $y = mx + b$?
5. How do you graph a linear equation using its slope and y-intercept?

Tip: Always double-check your calculations with more than one set of points to ensure consistency.