A line passes through $(2, 9)$ $(2 ,9 )$ and $(5, 2)$ $(5 ,2 )$ . A second line passes through $(3, 8)$ $(3 ,8 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

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A line passes through $(2, 9)$ $(2 ,9 )$ and $(5, 2)$ $(5 ,2 )$ . A second line passes through $(3, 8)$ $(3 ,8 )$ . 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 · 2017-01-02T17:27:48

Answer: $(0, 15)$ $(0, 15)$

Explanation:

First, find the slope of the first line by using

$slope = m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $"slope" = m = (y_2 - y_1) / (x_2 - x_1)$

In this case, you have

$m = \frac{2 - 9}{5 - 2} = - \frac{7}{3}$ $m = (2 - 9)/(5 -2)= -7/3$

Now with the slope of $- \frac{7}{3}$ $-7/3$ , we have to find two coordinates with the exact same slope. So we put it in the slope formula

$\frac{8 - ?}{3 - ?} = - \frac{7}{3}$ $(8- ?)/(3 - ?) = -7/3$

which is the slope we have to find. We could use $15$ $15$ and $0$ $0$ , and when we input them back into the equation the slope equals $- \frac{7}{3}$ $-7/3$ .

But since the slope formula is $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (y_2 - y_1) / (x_2 - x_1)$ , we often get confused and say $(15, 0)$ $(15,0)$ and forget it's $y$ $y$ over $x$ $x$ . So remember to switch them so $x = 0$ $x=0$ and $y = 15$ $y=15$ .

To continue, if something is parallel to another line they have the same slope.

If something is perpendicular it has the opposite reciprocal slope.

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A line passes through $(2, 9)$ $(2 ,9 )$ and $(5, 2)$ $(5 ,2 )$ . A second line passes through $(3, 8)$ $(3 ,8 )$ . 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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Impact of this question

Science

Math

Humanities

... and beyond

A line passes through (2,9)(2 ,9 ) and (5,2)(5 ,2 ). A second line passes through (3,8)(3 ,8 ). 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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Impact of this question

A line passes through $(2, 9)$ $(2 ,9 )$ and $(5, 2)$ $(5 ,2 )$ . A second line passes through $(3, 8)$ $(3 ,8 )$ . What is one other point that the second line may pass through if it is parallel to the first line?