What is the slope of any line perpendicular to the line passing through #(-15,2)# and #(-10,4)#?

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Answer 1 · 2017-01-16T03:43:03

The slope of the perpendicular line is #-5/2#

First, we need to determine the slope of the line going through the two points given in 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 two points from the problem gives:

#m = (color(red)(4) - color(blue)(2))/(color(red)(-10) - color(blue)(-15))#

#m = (color(red)(4) - color(blue)(2))/(color(red)(-10) + color(blue)(15))#

#m = (2)/(5)#

The slope of a perpendicular line is the negative inverse, so we "flip" the slope and take its negative:

#m_p = -5/2#