The equation you've provided is:

$-4x - 2y = 8$

This is a linear equation in two variables, $x$ and $y$. Let's solve for $y$ in terms of $x$.

Step 1: Isolate the $y$-term

First, we'll move the $-4x$ term to the right side of the equation: $-2y = 4x + 8$

Step 2: Solve for $y$

Now, divide both sides of the equation by $-2$ to solve for $y$: $y = \frac{4x + 8}{-2}$ $y = -2x - 4$

So the equation in slope-intercept form is: $y = -2x - 4$

This means the slope of the line is $-2$, and the y-intercept is $-4$.

Would you like more details or have any questions? Here are some related questions for further exploration:

1. What is the slope of the line represented by the equation $y = -2x - 4$?
2. How would the graph of this equation look on a coordinate plane?
3. Can you rewrite the equation in standard form $Ax + By = C$?
4. What are the x- and y-intercepts of the line $-4x - 2y = 8$?
5. How would you solve for $x$ if a specific $y$-value is given?

Tip: In linear equations, the slope $m$ can tell you how steep the line is, and the y-intercept $b$ gives the point where the line crosses the y-axis.