What is the slope of any line perpendicular to the line passing through #(1,-7)# and #(3,-5)#?

1 Answer
Jun 14, 2017

Answer:

See a solution process below:

Explanation:

First, we need to find the slope of the line passing 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)(-5) - color(blue)(-7))/(color(red)(3) - color(blue)(1)) = (color(red)(-5) + color(blue)(7))/(color(red)(3) - color(blue)(1)) = 2/2 = 1#

Let us call the slope of a perpendicular line #m_p#

The formula for the slope of a perpendicular line is: #m_p = -1/m#

Substituting the slope we calculated gives us the slope of the perpendicular line as:

#m_p = -1/1 = -1#