What is the slope of any line perpendicular to the line passing through #(-6,5)# and #(-8,10)#?

1 Answer
Mar 24, 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)(10) - color(blue)(5))/(color(red)(-8) - color(blue)(-6)) = (color(red)(10) - color(blue)(5))/(color(red)(-8) + color(blue)(6)) = 5/-2 = -5/2#

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)(-5/2) = 2/5#