# A line passes through (4 ,3 ) and (2 ,5 ). A second line passes through (5 ,6 ). What is one other point that the second line may pass through if it is parallel to the first line?

Mar 29, 2018

(3,8)

#### Explanation:

So we first have to find the direction vector between (2,5) and (4,3)

$\left(2 , 5\right) - \left(4 , 3\right) = \left(- 2 , 2\right)$

We know that a vector equation is made up of a position vector and a direction vector.

We know that (5,6) is a position on the vector equation so we can use that as our position vector and we know that it is parallel the other line so we can use that direction vector

$\left(x , y\right) = \left(5 , 6\right) + s \left(- 2 , 2\right)$

To find another point on the line just substitute any number into s apart from 0 so lets choose 1

$\left(x , y\right) = \left(5 , 6\right) + 1 \left(- 2 , 2\right) = \left(3 , 8\right)$

So (3,8) is another another point.