A line passes through $(6, 2)$ $(6 ,2 )$ and $(1, 3)$ $(1 ,3 )$ . A second line passes through $(1, 4)$ $(1 , 4 )$ . 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 · 2018-05-19T08:41:15

One other point that satisfies the second equation is $(11, 2)$ $(11,2)$

Slope of first line $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (y_2-y_1) / (x_2 - x_1)$

$m = \frac{3 - 2}{1 - 6} = - \frac{1}{5}$ $m = (3-2)/(1-6) = -1/5$

Since both the lines are parallel, slopes are equal.

Therefore slope of second line is also $= m = - (\frac{1}{5})$ $= m = -(1/5)$

Equation of second line is

$y - 4 = - (\frac{1}{5}) (x - 1)$ $y - 4 = -(1/5) (x-1)$

$x + 5 y = 21$ $x + 5y = 21$

For $y = 2, x = 11$ $y = 2, x = 11$

A line passes through (6,2)(6 ,2 ) and (1,3)(1 ,3 ). A second line passes through (1,4)(1 , 4 ). What is one other point that the second line may pass through if it is parallel to the first line?