A line passes through #(4 ,3 )# and #(2 ,1 )#. A second line passes through #(1 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2016-09-06T06:27:36

Equation of line passing through #(1,8)# and parallel to one passing through #(4,3)# and #(2,1)# is #x-y+7=0#

The slope of the line joining points #(4,3)# and #(2,1)# is

#(2-4)/(1-3)=-2/-2=1#

Any line parallel to it too will have a slope of #1#.

As equation of a line passing throuh #(x_1,y_1)# having slope #m# is given by #(y-y_1)=m(x-x_1)#.

Hence equation of second line passing through #(1,8)# and having a slope #1# is #y-8=1xx(x-1)#

or #y-8=x-1#

or #x-y+7=0#