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.

Learn how to solve the linear equation -4x - 2y = 8 by converting it into slope-intercept form. Understand the key concepts of algebra, including slope, y-intercept, and linear equations. This problem is suitable for students in Grades 8-10.

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