What is the slope of any line perpendicular to the line passing through #(-2,5)# and #(-3,1)#?

1 Answer
Mar 14, 2018

Answer:

See a solution process below:

Explanation:

First, we need to determine the slope of the line going through 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)(1) - color(blue)(5))/(color(red)(-3) - color(blue)(-2)) = (color(red)(1) - color(blue)(5))/(color(red)(-3) + color(blue)(2)) = (-4)/-1 = 4#

Now, 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)(4) = -1/4#