A line passes through $(6, 4)$ $(6 ,4 )$ and $(9, 2)$ $(9 ,2 )$ . A second line passes through $(3, 1)$ $(3 ,1 )$ . 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: $(1; \frac{7}{3})$ $(1;7/3)$

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: $(1;7/3)$

A line passes through (6 ,4 )(6,4)(6 ,4 ) and (9 ,2 )(9,2)(9 ,2 ). A second line passes through (3 ,1 )(3,1)(3 ,1 ). What is one other point that the second line may pass through if it is parallel to the first line?