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

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A line passes through $(3, 6)$ $(3 ,6 )$ and $(4, 7)$ $(4 ,7 )$ . A second line passes through $(7, 3)$ $(7 ,3 )$ . 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 · 2016-03-26T21:41:08

$(8, 4)$ $(8, 4)$

Explanation:

The slope $m$ $m$ of the line passing through $(x_{1}, y_{1}) = (3, 7)$ $(x_1, y_1) = (3, 7)$ and $(x_{2}, y_{2}) = (4, 7)$ $(x_2, y_2) = (4, 7)$ is given by the formula:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{7 - 6}{4 - 3} = \frac{1}{1} = 1$ $m = (y_2-y_1)/(x_2-x_1) = (7-6)/(4-3) = 1/1 = 1$

So a line through $(x_{0}, y_{0}) = (7, 3)$ $(x_0, y_0) = (7, 3)$ parallel to the first line will also have slope $1$ $1$ . Its equation can be written in point slope form as follows:

$y - y_{0} = m (x - x_{0})$ $y - y_0 = m(x - x_0)$

That is:

$y - 3 = 1 (x - 7)$ $y - 3 = 1(x - 7)$

Which we can rearrange in slope intercept form as:

$y = 1 x - 4$ $y = 1x-4$

Putting $x = 8$ $x=8$ we get: $y = 8 - 4 = 4$ $y = 8-4 = 4$

So the second line passes through $(8, 4)$ $(8, 4)$

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

1 Answer

Explanation:

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Science

Math

Humanities

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

1 Answer

Explanation:

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