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

1 Answer
Dec 19, 2016

Answer:

The slope of any perpendicular line will be: #4/19#

Explanation:

First, we need to determine the slope of the line for the two given points.

The slope can be found by using the formula: #color(red)(m = (y_2 = y_1)/(x_2 - x_1)#
Where #m# is the slope and #(x_1, y_1)# and #(x_2, y_2)# are the two points.

Substituting the points provided gives:

#m = (-13 - 6)/(-2 - - 6)#

#m = (-19)/(-2 + 6)#

#m = (-19)/(4)#

#m = -19/4#

The slope of a line perpendicular to a given line is the negative inverse of the slope of the given line.

So, if the slope of a given line is:

#m#,

the slope of a perpendicular line is:

#-1/m#

For our problem, the slope of the given line is:

#-19/4#

Therefore, the slope of a perpendicular line is:

#-1 xx -4/19#

#4/19#