Which equation represents a line which is parallel to the line 2x+y=-8?

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!

Which equation represents a line which is parallel to the line 2x + y = -8?

Discover how to find the equation of a line parallel to 2x + y = -8 by identifying the slope and applying it to new lines. This problem focuses on algebraic concepts of slope and parallel lines, suitable for students in Grades 8-10.

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