Final answer:
Option C. To find a line parallel to 2y - 5x = 10, we rearrange the given equation to find its slope, which is 5/2. Then, we find that option (c) 2y + 5x = 15, when rearranged, has the same slope of 5/2 and is therefore the parallel line.
Step-by-step explanation:
The question is about finding a line parallel to the given line, with the equation 2y - 5x = 10. For two lines to be parallel, they must have the same slope. When looking at the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept, we can identify the slope by arranging the given equation into this form.
If we rearrange the given equation into y = mx + b form, we get y = (5/2)x + 5. The slope here is 5/2. Now we need to check which of the given options, when rearranged into y = mx + b form, have the same slope of 5/2. After rearranging each of the options, we will see that option (c) 2y + 5x = 15 can be written as y = (-5/2)x + 7.5, which has the same slope of 5/2, and thus it represents a line parallel to the given line.