What is the slope of any line perpendicular to the line passing through #(7,-9)# and #(-5,-3)#?

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Answer 1 · 2018-04-17T10:29:03

#2#
#y = 2x - 23#

If by slope you mean gradient, then first work out the gradient of the line that goes through those points:

#"change in y"/"change in x" = "gradient"#

#((-9) - (-3))/ (7 - (-5)) = (-6) / 12 = -0.5# (as #(--) = +#)

The perpendicular gradient will be the negative reciprocal (meaning when multiplied together it produces #-1#). This is also known as the 'normal'.

Normal of #-0.5 = 2#

Therefore, gradient is #2# of the perpendicular line to the line which passes through those 2 points.

If you want the equation of one of those lines then:

#y - (-9) = 2 " x " ( x - 7)#
#y + 9 = 2x - 14#

#y = 2x -23#