What is the slope of any line perpendicular to the line passing through #(-2,8)# and #(0,4)#?

1 Answer
Oct 4, 2017

Answer:

See a solution process below:

Explanation:

First, we need to determine the slope of the line passing 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)(4) - color(blue)(8))/(color(red)(0) - color(blue)(-2)) = (color(red)(4) - color(blue)(8))/(color(red)(0) + color(blue)(2)) = -4/2 = -2#

Now, let's call the perpendicular slope #m_p#. The formula for the perpendicular slope is:

#m_p = -1/m#

Substituting the slope we calculated for #m# gives:

#m_p = (-1)/(-2)#

#m_p = 1/2#