What is the slope of a line parallel and perpendicular to the line going through: #(-7, -3)# and #(6, 8)#?

1 Answer
Apr 10, 2017

Answer:

See the entire solution process below:

Explanation:

First, find the slope of the line going through the two points. 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 values from the points in the problem gives:

#m = (color(red)(8) - color(blue)(-3))/(color(red)(6) - color(blue)(-7)) = (color(red)(8) + color(blue)(3))/(color(red)(6) + color(blue)(7)) = 11/13#

A line parallel to this line will have the same slope as this line. Therefore, the slope of a parallel line will be: #m = 11/13#

Let's call the slope of a perpendicular line #m_p#. The slope of a perpendicular line is:

#m_p = -1/m#

Therefore, the slope of a perpendicular line is: #m_p = -13/11#