A line passes through $(3, 6)$ $(3 ,6 )$ and $(6, 5)$ $(6 ,5 )$ . A second line passes through $(4, 3)$ $(4 ,3 )$ . 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 · 2016-03-21T16:05:49

$(1, 4)$ $(1,4)$ for instance

The slope of the first equation is
$k_1=(Delta y)/(Delta x)=(5-6)/(6-3)=-1/3$

$y-6=-1/3(x-3)$ => $y=(-x+3)/3+6$ => $y=(-x+21)/3$

$k_2=k_1=-1/3$

$y-3=-1/3(x-4)$ => $y=(-x+4)/3+3$ => $y=(-x+13)/3$

Since the equation of second line is $y=(-x+13)/3$
For instance with $x=1$
$-> y=(-1+13)/3=4$
$-> (1,4)$

A line passes through (3 ,6 )(3,6)(3 ,6 ) and (6 ,5 )(6,5)(6 ,5 ). A second line passes through (4 ,3 )(4,3)(4 ,3 ). What is one other point that the second line may pass through if it is parallel to the first line?