What is the slope of any line perpendicular to the line passing through #(-2,6)# and #(9,-13)#?

1 Answer
smendyka
Feb 7, 2017

The slope of a perpendicular line is #11/19#

Explanation:

First, we need to determine the slope of the line passing through these two points. 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 values from the points in the problem gives:

#m = (color(red)(-13) - color(blue)(6))/(color(red)(9) - color(blue)(-2))#

#m = (color(red)(-13) - color(blue)(6))/(color(red)(9) + color(blue)(2))#

#m = -19/11#

The slope of a perpendicular line, let's call it #m_p# is the negative inverse of the slope of the line it is perpendicular to. Or #m_p = =1/m#

Therefore the slope of a perpendicular line in this problem is:

#m_p = - -11/19#

#m_p = 11/19#

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