A line passes through (5 ,8 )(5,8) and (2 ,2 )(2,2). A second line passes through (1 ,3 )(1,3). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Alan P.
Jun 1, 2016

(0,1)(0,1) is one possible point on the second line

Explanation:

If a line L_1L1 passes through (5,8)(5,8) and (2,2)(2,2)
it has a slope m_1= (Deltay)/(Deltax)=(8-2)/(5-2)=2

If L_2 is parallel to L_1 it must have the same slope
color(white)("XXX")m_2=2

If L_2 passes through (1,3) and has a slope of m_2=2
its equation can be written in slope point form as
color(white)("XXX")(y-3)=2(x-1)
or, more concisely as
color(white)("XXX")y=2x+1

Setting x=0 (for example) gives y=1
so (0,1) would be another point on the second line l_2

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