Final answer:
The slope of the given line is -5, so the parallel line must also have a slope of -5. Since it passes through (0, -5), the y-intercept is -5. Thus, the equation of the parallel line is y = -5x - 5, which doesn't match any of the provided options.
Correct option is not given .
Step-by-step explanation:
The equation of the given line is 10x + 2y = -2. To find the slope-intercept form, we solve for y:
2y = -10x - 2
y = -5x - 1
Here, the slope (m) is -5 and the y-intercept (b) is -1. Since parallel lines have the same slope, the slope of the line we are looking for is also -5. The line must pass through the point (0, -5), so this is its y-intercept.
Therefore, the equation of the line in slope-intercept form is:
y = -5x + (-5)
y = -5x - 5
Comparing this with the provided options, none of them directly match this equation, indicating a potential typo in the question.
However, if the question intended to have the expression 'y = -5x - 5' amongst the options, we would select it as the correct answer.
Correct option is not given .