A line passes through $(5, 9)$ $(5 ,9 )$ and $(8, 3)$ $(8 ,3 )$ . 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 · 2018-04-06T11:57:30

One other point on the second line is $(0, 7)$ $(0,7)$

![https://www.ck12.org/geometry/Parallel-Lines-in-the-Coordinate-Plane/](https://useruploads.socratic.org/5eof64GFSk6cvzwx2dz4_Parallel%20lines.1)

$Equation of line 1 is \frac{y - 9}{3 - 9} = \frac{x - 5}{8 - 5}$ $"Equation of line 1 is " (y - 9) / (3-9) = (x - 5) / (8 - 5)$

$(y - 9) / cancel(-6)^color(red)(-2) = (x - 5) / cancel3$

$y - 9 = -2x + 10$

$y = -2x + 19, " where -2 is the slope$

Since the lines are parallel, their slopes will be equal .

$:. "Equation of "2^(nd) " line is " y - 1 = m * (x - 3)$

$y - 1 = -2 (x - 3)$

$y = -2x + 7$

When $x = 0, y = 7$

Hence one other point is $(0,7)$

A line passes through (5 ,9 )(5,9)(5 ,9 ) and (8 ,3 )(8,3)(8 ,3 ). 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?