Final answer:
The line parallel to the given equation y = -5/2x - 7 is the one with the same slope, which is Option C: 5x + 2y = 4, because it rearranges to y = -5/2x + 2 with a slope of -5/2.
Step-by-step explanation:
The question asks which line is parallel to the line given by the equation y = -5/2x - 7. Two lines are parallel if they have the same slope. The slope of the given line is -5/2. We need to find which of the provided equations has the same slope.
- Option A: Rearranging 2x + 5y = -5 into slope-intercept form gives us y = -2/5x - 1, which does not have the same slope.
- Option B: Rearranging 2x - 5y = 30 into slope-intercept form gives us y = 2/5x - 6, which also does not have the same slope.
- Option C: Rearranging 5x + 2y = 4 into slope-intercept form gives us y = -5/2x + 2, which has the same slope of -5/2 and is therefore parallel to the given line.
- Option D: Rearranging 5x - 2y = 8 into slope-intercept form gives us y = 5/2x - 4, which does not have the same slope.
The correct answer is Option C: 5x + 2y = 4.