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Parallel lines have the same slope. So if you know the slope of a line in question, or you can calculate it, then you know the slope of any line parallel to that line.
For two lines to be parallel they must have the same slope. A line parallel to a line with slope -2 would have a slope of -2.
if the slope of a line is 2/3, then the slope of a parallel line would be 2/3.
The parallel line would also have a slope of zero (both are horizontal lines).
The parallel line will have the same slope or gradient but with a different y intercept