What is the slope of any line perpendicular to the line passing through (-6,1) and (7,-2)?

1 Answer
Apr 7, 2018

See a solution process below:

Explanation:

The formula for find the slope of a line is:

m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))

Where (color(blue)(x_1), color(blue)(y_1)) and (color(red)(x_2), color(red)(y_2)) are two points on the line.

Substituting the values from the points in the problem gives:

m = (color(red)(-2) - color(blue)(1))/(color(red)(7) - color(blue)((-6))) = (color(red)(-2) - color(blue)(1))/(color(red)(7) + color(blue)(6)) = -3/13

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)(-3/13) = 13/3