A line passes through #(6 ,4 )# and #(9 ,2 )#. A second line passes through #(3 ,1 )#. 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 · 2017-01-14T07:38:11

another point of the second line is: #(1;7/3)#

A line parallel to another one has the same slope, then you can find the slope m of the first line by the following formula:

#m=(Deltay)/(Deltax)=(2-4)/(9-6)=-2/3#

where #Deltay# is the difference between the y-coordinates of the given points and #Deltax# is the difference between their x-coordinates.

To find another point of the second line you can choose one coordinate and find the second, depending on the chosen one:

Then if you decide, for example, to choose #color(red)(x=1)#, you would solve:

#(Deltay)/(Deltax)=(1-y)/(3-color(red)1)=-2/3#

where(3;1) is the given point of the second line.

That's

#3*(1-y)=-2*2#

#3-3y=-4#

#y=7/3#

Then another point of the second line is: #(1;7/3)#