How do you determine if the lines through the given points (4,6), (5,3) are parallel and which, if any, are perpendicular?

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Answer 1 · 2016-11-16T18:44:00

Please see the explanation.

In general, a line is parallel to another line, if the two lines have the same slope:

#n = m#

A line will be perpendicular to another line if the slope, n of the perpendicular line has the following relationship to the slope, m:

#n = -1/m#

The slope of a line between the two points is:

#m = (3 - 6)/(5 - 4) = -3#

If a line is parallel to the line between these two points, its slope will be #-3#.

If the line is perpendicular, its slope is #1/3#