How do you write an equation in point-slope form for the given (3, -2), (5, 4)?

1 Answer
Alan P.
Aug 8, 2015

#y -4 = 3(x-5)#

Explanation:

Given two points #(x_1,y_1)# and #(x_2,y_2)#
the slope is given by
#color(white)("XXXX")##m = (y_2-y_1)/(x_2-x_1)#

For the given points #(3,-2)# and #(5,4)#
this becomes
#color(white)("XXXX")##m= (4-(-2))/(5-3) = 6/2 = 3#

The general slope-point form is
#color(white)("XXXX")##(y-haty) = m(x-hatx)#
and we can use either of the given points for #(hatx, haty)#

Using #(5,4)# as #(hatx, haty)#
we have
#color(white)("XXXX")##y -4 = 3(x-5)#
as our point-slope form

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