How do you find the slope that is perpendicular to the line (-3,6) (9,7)?

1 Answer
smendyka
Jan 26, 2017

See the entire solution process below:

Explanation:

First, find the slope of this line using the two points from the problem.

The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the points from the problem gives:

#m = (color(red)(7) - color(blue)(6))/(color(red)(9) - color(blue)(-3))#

#m = (color(red)(7) - color(blue)(6))/(color(red)(9) + color(blue)(3))#

#m = 1/12#

The slope of a perpendicular line will be the negative inverse, or #-1/m# of the given line. Taking the negative inverse of the slope we calculated gives:

#-12/1 = -12#

The slope of a perpendicular line will be #-12#

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