What is the slope of any line perpendicular to the line passing through #(13,7)# and #(7,-2)#?

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Answer 1 · 2018-06-11T20:05:39

See a solution process below:

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)(7))/(color(red)(7) - color(blue)(13)) = (-9)/-6 = 9/6 = 3/2#

Now, 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)(3/2) = -2/3#