Final answer:
To find a line parallel to the given line, we need to find its slope. The slope of the given line is -0.5. None of the answer choices represent a line with the same slope, so none of them are parallel to the given line.
Step-by-step explanation:
In order to find the equation of a line parallel to the line x + 2y = -6, we need to find the slope of the given line. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope. To convert the given equation into slope-intercept form, we can isolate y by subtracting x from both sides of the equation: 2y = -x - 6. Dividing both sides by 2 gives us y = -0.5x - 3. Therefore, the slope of the given line is -0.5.
Since parallel lines have the same slope, the equation of the parallel line will also have a slope of -0.5. Let's evaluate the given answer choices:
- a. y = -2x - 4: The slope of this line is -2, which is not equal to -0.5. It is not parallel to the given line.
- b. y = 2x - 8: The slope of this line is 2, which is not equal to -0.5. It is not parallel to the given line.
- c. y = 1/2x - 6: The slope of this line is 1/2, which is not equal to -0.5. It is not parallel to the given line.
- d. y = 1/2 + 4: This equation does not represent a line in the slope-intercept form. It is not parallel to the given line.
None of the given answer choices represent a line that is parallel to x + 2y = -6.