To find an equation that represents a line parallel to the line $2x + y = -8$, we need to ensure the new line has the same slope.

First, let's rewrite the given equation in slope-intercept form $y = mx + b$, where $m$ is the slope:

$2x + y = -8 \quad \text{(Original equation)}$ $y = -2x - 8 \quad \text{(Solving for } y \text{)}$

From this, we can see that the slope $m$ is $-2$.

For a line to be parallel, it must have the same slope. Therefore, the equation of any line parallel to this one will have the form:

$y = -2x + c$

Where $c$ can be any constant representing the y-intercept.

Example:

An example of a parallel line could be: $y = -2x + 5$

This line is parallel to $2x + y = -8$ because it has the same slope $-2$.

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Do you want more details on how to find parallel or perpendicular lines?

Here are 5 related questions:

1. How do you find the slope of a line from its equation?
2. How can you determine if two lines are perpendicular?
3. What is the slope of a vertical line?
4. How do you find the equation of a line given a point and the slope?
5. What are the key differences between parallel and coincident lines?

Tip: Parallel lines never intersect because they have identical slopes!