How do you write an equation of a line that contains the points (2, 3) and (3, 2)?

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Answer 1 · 2017-05-25T22:37:50

#x + y = 5#

Is it vertical? No. Then it is a function.

#f(x) = ax + b#
#f(2) = 3 and f(3) = 2#

#2a + b = 3 and 3a + b = 2#

Subtracting we cancel #b#:

#2a + b - 3a - b = 3 - 2#

#-a = 1#
#a = -1#

From the first:

#2(-1) + b = 3#
#-2 + b = 3#
#b = 3 + 2 = 5#

#f(x) = -x + 5#