What is the equation of the line that goes through #A( 1,- 5)# and # B ( 7,3)#?

2 Answers
Cem Sentin
Nov 28, 2017

#4x-3y=19#

Explanation:

After using line equation which goes through 2 points,

#(y-3)/(x-7)=(3-(-5))/(7-1)#

#(y-3)/(x-7)=8/6#

#(y-3)/(x-7)=4/3#

#3*(y-3)=4*(x-7)#

#3y-9=4x-28#

#4x-3y=19#

Grimalkyne
Nov 28, 2017

#y =( 4x)/3 -19/3# or could be re-written as #3y = 4x -19#

Explanation:

The general formula for a straight line is
#y = mx + c# where #m# is the slope and #c# is the #y# intercept (the point at which the line crosses the y axis#

Given two points the slope can be calculated as
#m=(y_2-y_1)/(x_2-x_1)#

Substitute in what we know
#m = (3--5)/(7-1) = 8/6 = 4/3#

so now we have
#y =( 4x)/3 +c#

To calculate c, substitute #x# and #y# for one of the points given
#3 =4*7/3 + c#

Multiply throughout by 3
#9 = 28 + 3c#

And simplify
#-19 = 3c#

#c = -19/3#

our equation now looks like
#y =( 4x)/3 -19/3# or could be re-written as #3y = 4x -19#

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