What is the slope of any line perpendicular to the line passing through #(-8,23)# and #(5,21)#?

1 Answer
Jun 14, 2018

Answer:

See a solution process below:

Explanation:

The formula for find the slope of a line is:

#m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

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

Substituting the values from the points in the problem gives:

#m = (color(red)(21) - color(blue)(23))/(color(red)(5) - color(blue)(-8)) = (color(red)(21) - color(blue)(23))/(color(red)(5) + color(blue)(8)) = -2/13#

Let's call the slope of a perpendicular line: #color(blue)(m_p)#

The slope of a line perpendicular to a line with slope #color(red)(m)# is the negative inverse, or:

#color(blue)(m_p) = -1/color(red)(m)#

Substituting the slope for the line in the problem gives:

#color(blue)(m_p) = (-1)/color(red)(-2/13)= 1/color(red)(2/13) = 13/2#