What is the equation of the line passing through #(3,4)# and #(9,19)#?

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Answer 1 · 2015-11-18T02:52:28

#y = 5/2x - 7/2#

First, get the slope

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

#=> m = (4 - 19)/(3 - 9)#

#=> m = -15/-6#

#=> m = 5/2#

Next, get the #y#-intercept. We do this by plugging-in any of the given points

#y = mx + b#

#=> 4 = 5/2(3) + b#

#=> 4 = 15/2 + b#

#=> b = 4 - 15/2#

#=> b = (8 - 15)/2#

#=> b = -7/2#

Hence, the equation of the line passing through the points #(3, 4)# and #(9, 19)# is

#y = 5/2x - 7/2#