What is the slope of any line perpendicular to the line passing through #(1,-2)# and #(18,11)#?

1 Answer
Mar 14, 2018

Answer:

See a solution process below:

Explanation:

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)(11) - color(blue)(-2))/(color(red)(18) - color(blue)(1)) = (color(red)(11) + color(blue)(2))/(color(red)(18) - color(blue)(1)) = 13/17#

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)(13/17) = -17/13#