What is the equation of the line between #(5,-6)# and #(2,-2)#?

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Answer 1 · 2016-04-13T17:44:28

#y = -4/3x +2/3#

The formula for the slope of a line based upon two coordinate points is

#m = (y_2-y_1)/(x_2-x_1)#

For the coordinate points #(5,-6) and (2,-2)#
#x_1 = 5#
#x_2 = 2#
#y_1 = -6#
#y_2 = -2#

#m = (-2-(-6))/(2-5)#

#m = 4/-3#

The slope is #m = -4/3#

The point slope formula would be written as
#y - y_1 = m( x - x_1)#

#m = -4/3#
#x_1 = 2#
#y_1=-2#

#y - (-2) = -4/3 (x -2)#

#y + 2 = -4/3x +8/3#

#y cancel(+ 2) cancel(- 2)= -4/3x +2(2)/3 -2#

#y = -4/3x +2/3#