Final answer:
The slope of any line parallel to the line passing through the points (3,-6) and (-5,2) is -1, as parallel lines have the same slope.
Step-by-step explanation:
To find the slope of a line parallel to the line passing through the points (3,-6) and (-5,2), we first need to calculate the slope of the given line. The formula for finding the slope (m) given two points (x1, y1) and (x2, y2) is: m = (y2 - y1) / (x2 - x1).
Substitute the given points into the formula: m = (2 - (-6)) / (-5 - 3) = 8 / -8 = -1. So, the slope of the line passing through the points (3,-6) and (-5,2) is -1.
Now, parallel lines have the same slope. So, the slope of any line parallel to the line passing through the points (3,-6) and (-5,2) is also -1.
Learn more about Slope of Parallel Lines