A line passes through $(4, 9)$ $(4 ,9 )$ and $(6, 1)$ $(6 ,1 )$ . A second line passes through $(7, 5)$ $(7 ,5 )$ . 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 · 2017-03-03T18:17:31

$it may be any point on the red line$ $"it may be any point on the red line"$

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$the parallel lines have the same slope$ $"the parallel lines have the same slope"$

$m_{r} = \frac{9 - 1}{4 - 6} = \frac{8}{- 2} = - 4 ( the red line's slope)$ $m_r=(9-1)/(4-6)=8/-2=-4" ( the red line's slope)"$

$m_{b} = - 4 (the red line's slope)$ $m_b=-4 " (the red line's slope)"$

$- 4 = \frac{y - 5}{x - 7}$ $-4=(y-5)/(x-7)$

$- 4 x + 28 = y - 5$ $-4x+28=y-5$

$4 x + y = 28 + 5$ $4x+y=28+5$

$4 x + y = 33$ $4x+y=33$

$it may be any point on the red line$ $"it may be any point on the red line"$

$for example :$ $"for example :"$

$if x=6 then 4 \cdot 6 + y = 33$ $"if x=6 then " 4*6+y=33$

$y = 33 - 24 = 9$ $y=33-24=9$

$P (6, 9)$ $P(6,9)$

A line passes through (4,9)(4 ,9 ) and (6,1)(6 ,1 ). A second line passes through (7,5)(7 ,5 ). What is one other point that the second line may pass through if it is parallel to the first line?