How do you find a standard form equation for the line with A(4,-6); B(-2,8)?

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Answer 1 · 2016-08-31T00:50:44

#7x+3y-10=0#

The standard form of equation of a line is #ax+by+c=0#.

The equation of a line joining two points #(x_1,y_1)# and #(x_2,y_2)# is given by

#(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)#.

Hence equation of line joining #A(4,-6)# and #B(-2,8)# is

#(y-(-6))/(8-(-6))=(x-4)/(-2-4)# or

#(y+6)/14=(x-4)/(-6)# or

#14×(x-4)=(-6)×(y+6)# or

#14x-56=-6y-36# or

#14x+6y-56+36=0# or

#14x+6y-20=0# or diving by #2#

#7x+3y-10=0#