What is the slope of any line perpendicular to the line passing through #(-5,1)# and #(11,-4)#?

1 Answer
Jan 30, 2016

Answer:

A line #b# perpendicular to another line #a# has a gradient of #m_b = -1/m_a# where #m_a# is the gradient (slope) of line #a#. In this case the slope is #(16)/5#.

Explanation:

To find the gradient (slope) of the given line through the points #(-5, 1)# and #(11, -4)# use the formula:

#m=(y_2-y_2)/(x_2-x_1) = (-4-1)/(11-(-5)) = -5/16#

Lines parallel to this line will have the same slope, lines perpendicular to it will have slope #-1/m#.

In this case, that means the slope of any perpendicular line will be #(16)/5#.