A line passes through $(1, 5)$ $(1 ,5 )$ and $(8, 7)$ $(8 ,7 )$ . A second line passes through $(3, 6)$ $(3 ,6 )$ . 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 $(1, 5)$ $(1 ,5 )$ and $(8, 7)$ $(8 ,7 )$ . A second line passes through $(3, 6)$ $(3 ,6 )$ . 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 · 2018-02-20T01:56:55

$(10, 8)$ $(10,8)$

Explanation:

I didn't use math to figure this out, but I'll explain both ways. First the easy way.

To get from $(1, 5)$ $(1,5)$ to $(3, 6)$ $(3,6)$ , you increase $x$ $x$ by $2$ $2$ and $y$ $y$ by $1$ $1$ , so if you do the same thing to $(8, 7)$ $(8,7)$ , you get $(10, 8)$ $(10,8)$ . If you move both points by the same amount, the slope stays the same.

Mathematically, you would have to find the slope of the line made by $(1, 5)$ $(1,5)$ and $(8, 7)$ $(8,7)$ . So you do the slope formula, and you get

$slope = m = \frac{7 - 5}{8 - 1}$ $"slope" = m = (7-5)/(8-1$

which equals $\frac{2}{9}$ $2/9$ . Then you use the point-slope formula and input $(3, 6)$ $(3,6)$ for the $x$ $x$ and $y$ $y$ variables and $\frac{2}{9}$ $2/9$ for the $m$ $m$ variable.

You end up with

$y - 6 = (\frac{2}{7}) (x - 3)$ $y-6=(2/7)(x-3)$

which, when you solve for $y$ $y$ , becomes

$y = \frac{2}{7} x + \frac{36}{7}$ $y=2/7x+36/7$

(I kept the fractions so it would be easier to solve).

Then just pick an $x$ $x$ value and plug it in yo get your $y$ $y$ and you're done. Yay! (You'll notice that plugging in $10$ $10$ gets you $\frac{56}{7}$ $56/7$ , which is $8$ $8$ )

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A line passes through $(1, 5)$ $(1 ,5 )$ and $(8, 7)$ $(8 ,7 )$ . A second line passes through $(3, 6)$ $(3 ,6 )$ . 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 (1 ,5 )(1,5)(1 ,5 ) and (8 ,7 )(8,7)(8 ,7 ). A second line passes through (3 ,6 )(3,6)(3 ,6 ). 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 $(1, 5)$ $(1 ,5 )$ and $(8, 7)$ $(8 ,7 )$ . A second line passes through $(3, 6)$ $(3 ,6 )$ . What is one other point that the second line may pass through if it is parallel to the first line?