A line passes through $(3, 9)$ $(3 ,9 )$ and $(5, 1)$ $(5 ,1 )$ . A second line passes through $(7, 6)$ $(7 ,6 )$ . 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 $(3, 9)$ $(3 ,9 )$ and $(5, 1)$ $(5 ,1 )$ . A second line passes through $(7, 6)$ $(7 ,6 )$ . 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 · 2016-09-22T06:45:17

Any point other than $(7, 6)$ $(7,6)$ and satisfying the condition $4 x + y = 34$ $4x+y=34$ could be such a point. Examples are $(0, 34)$ $(0,34)$ , $(- 8, 66)$ $(-8,66)$ and $(12, - 14)$ $(12,-14)$ .

Explanation:

A line passing through $(x_{1}, y_{1})$ $(x_1, y_1)$ and $(x_{2}, y_{2})$ $(x_2, y_2)$ has a slope of $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $(y_2-y_1)/(x_2-x_1)$ . Hence slope of line joining $(3, 9)$ $(3,9)$ and $(5, 1)$ $(5,1)$ is

$\frac{1 - 9}{5 - 3} = - \frac{8}{2} = - 4$ $(1-9)/(5-3)=-8/2=-4$

As the second line passing through $(7, 6)$ $(7,6)$ is parallel to the above, its slope too is $- 4$ $-4$ .

Now, equation of a line passing through $(x_{1}, y_{1})$ $(x_1,y_1)$ and having a slope of $m$ $m$ is $(y - y_{1}) = m (x - x_{1})$ $(y-y_1)=m(x-x_1)$ . Hence, the equation of line passing through $(7, 6)$ $(7,6)$ and having a slope of $- 4$ $-4$ is

$(y - 6) = - 4 (x - 7)$ $(y-6)=-4(x-7)$ or $y - 6 = - 4 x + 28$ $y-6=-4x+28$ i.e. $4 x + y = 34$ $4x+y=34$

Hence, any point satisfying the condition $4 x + y = 34$ $4x+y=34$ (other than $(7, 6)$ $(7,6)$ will satisfy this.

Let $x = 0$ $x=0$ then $y = 34$ $y=34$ , hence point could be $(0, 34)$ $(0,34)$ or

let $x = - 8$ $x=-8$ then $y = 66$ $y=66$ , hence other point could be $(- 8, 66)$ $(-8,66)$ or

let $x = 12$ $x=12$ then $y = - 14$ $y=-14$ , hence point could be $(12, - 14)$ $(12,-14)$

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A line passes through $(3, 9)$ $(3 ,9 )$ and $(5, 1)$ $(5 ,1 )$ . A second line passes through $(7, 6)$ $(7 ,6 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

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Explanation:

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A line passes through (3,9)(3 ,9 ) and (5,1)(5 ,1 ). A second line passes through (7,6)(7 ,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 $(3, 9)$ $(3 ,9 )$ and $(5, 1)$ $(5 ,1 )$ . A second line passes through $(7, 6)$ $(7 ,6 )$ . What is one other point that the second line may pass through if it is parallel to the first line?