A line passes through $(6, 2)$ $(6 ,2 )$ and $(3, 4)$ $(3 ,4 )$ . A second line passes through $(7, 8)$ $(7 ,8 )$ . 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 · 2017-09-30T19:14:27

Some points can be $(1, 12), (4, 10), and (7, 8)$ $(1,12), (4,10), and (7,8)$

Slope of line between $(6, 2)$ $(6,2)$ and $(3, 4)$ $(3,4)$ = $\frac{2 - 4}{6 - 3} = - \frac{2}{3}$ $(2-4)/(6-3) = -2/3$

If a line has to pass through a point given the slope, we can use point-slope equation:

$y - y_{1} = s l o p e (x - x_{1})$ $y-y_1=slope(x-x_1)$

$y - 8 = - \frac{2}{3} (x - 7)$ $y-8=-2/3(x-7)$

$y = - \frac{2}{3} x + \frac{38}{3}$ $y=-2/3x+38/3$

Other points this can go through is $(1, 12), (4, 10), and (7, 8)$ $(1,12), (4,10), and (7,8)$

A line passes through (6,2)(6 ,2 ) and (3,4)(3 ,4 ). A second line passes through (7,8)(7 ,8 ). What is one other point that the second line may pass through if it is parallel to the first line?