What is the slope of any line perpendicular to the line passing through #(-5,1)# and #(-14,-4)#?

1 Answer
Aug 21, 2017

Answer:

See a solution process below:

Explanation:

First, we need to find the slope of the line containing the two points in the problem. 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)(-4) - color(blue)(1))/(color(red)(-14) - color(blue)(-5)) = (color(red)(-4) - color(blue)(1))/(color(red)(-14) + color(blue)(5)) = (-5)/-9 = 5/9#

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

The slope of a perpendicular line is:

#m_p = -1/m#

Substituting gives:

#m_p = -1/(5/9) = -9/5#