What is the slope of any line perpendicular to the line passing through #(2,15)# and #(10,21)#?

1 Answer
Aug 30, 2017

Answer:

See a solution process below:

Explanation:

First, we need to find 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)(21) - color(blue)(15))/(color(red)(10) - color(blue)(2)) = 6/8 = 3/4#

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

The slope of a perpendicular can be found using the formula:

#m_p = -1/m# (This is the negative inverse)

Substituting gives:

#m_p = -1/(3/4) = -4/3#