Problem 2042

The slope of a given line is shown below. Find the slope of a line parallel to the given line and the slope of a line perpendicular to the given line.

m = -12

 

Solution:-

 

First find the slop of a line parallel to the given line.

Two nonvertical lines are parallel of and only of their slope are equal and they have different y-intercepts. Vertical lines are parallel if they have different x-intercepts.

Therefore, the slope of a line parallel to the given line is m = -12.

Now find the slope of a line perpendicular to the given line.

Two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Put another way, two nonvertical lines are perpendicular if their slopes are negative reciprocals of each other. Any vertical line is perpendicular to any horizontal line.

To find the slop of a line perpendicular to a given line, determine the negative reciprocal of the slope of the given line.

The negative reciprocal of -12 is \frac{-1}{-12} or \frac{1}{12}.

Therefore, the slope of a line perpendicular to the given line is

m = \frac{1}{12}

 

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