A line passes through $(5, 8)$ $(5 ,8 )$ and $(2, 9)$ $(2 ,9 )$ . A second line passes through $(1, 5)$ $(1 ,5 )$ . 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 · 2016-03-28T03:22:50

One other point is $(16, 0)$ $(16,0)$

First we need to find the equation of the line passes through (5,8) and (2,9).The equation is

$y = \frac{29}{3} - \frac{x}{3}$ $y = 29/3-x/3$

The slope is $- \frac{1}{3}$ $-1/3$ so that is the slope of the requested line hence

$y = - \frac{1}{3} x + b$ $y=-1/3x+b$

Point $(x = 1, y = 5)$ $(x=1,y=5)$ satisfies the above equation hence

$5 = - \frac{1}{3} \cdot 1 + m \Rightarrow m = 5 + \frac{1}{3} \Rightarrow m = \frac{16}{3}$ $5=-1/3*1+m=>m=5+1/3=>m=16/3$

Last the equation is

$y = - \frac{x}{3} + \frac{16}{3}$ $y=-x/3+16/3$

Hence one other point is $(16, 0)$ $(16,0)$

A line passes through (5 ,8 )(5,8)(5 ,8 ) and (2 ,9 )(2,9)(2 ,9 ). A second line passes through (1 ,5 )(1,5)(1 ,5 ). What is one other point that the second line may pass through if it is parallel to the first line?