How do you write the equation in slope intercept form given (2,5) and (7,-3)?

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Answer 1 · 2016-05-16T19:25:21

The slope-intercept form of the equation of the line is
#y = -8/5x +25/5#

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 #(2,5) and (7,-3)#
#x_1 = 2#
#x_2 = 7#
#y_1 = 5#
#y_2 = -3#

#m = (-3-5)/(7-2)#

#m = -8/5#

The slope is #m = -8/5#

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

#m = -8/5#
#x_1 = 2#
#y_1=5#

#y - 5 = -8/5 (x -2)#

#y - 5 = -8/5x +16/5#

#y cancel(-5) cancel(+ 5)= -8/5x +16/5 +5#

#y = -8/5x +16/5 +25/5#

The slope-intercept form of the equation of the line is
#y = -8/5x +25/5#

The standard form would be
#5y = -8x +25#