Using any two points, calculate the differences in the Y and the X coordinates. Then take the difference between the Y and divide it by the difference in the X.
Example:
Points (1,3) and (4,9) are on a line. Determine the slope of the line.
X coordinates: 1 and 4.
4-1 = 3
Y coordinates: 3 and 9
9-3 = 6
Slope = Y/X = 6/3 = 2
The slope is 2
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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.
You need two coordinates, not one, to specify a point. To calculate the slope, simply calculate (difference in y-coordinates) / (difference in x-coordinates).
If the line has a slope of 2, then the perpendicular line has a slope of -1/2. The slope of a perpendicular line is the negative reciprocal. Another example would be if the slope of a line is -1/4, then the slope of the perpendicular is 4.
if the slope of a line is 2/3, then the slope of a parallel line would be 2/3.
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.