# A line passes through (2 ,5 ) and (0 ,1 ). A second line passes through (7 ,1 ). What is one other point that the second line may pass through if it is parallel to the first line?

Jun 21, 2018

$p \left(8 , 3\right)$ for example

#### Explanation:

First, find the slope of the first line.

$m = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}} = \frac{5 - 1}{2 - 0} = \frac{4}{2} = 2$

Because line 1 is parallel to line 2, they have the same slope.
Knowing that the slope of line 2 is $m = 2 = \frac{\textcolor{red}{2}}{\textcolor{b l u e}{1}}$ as well, another point would be $p \left(7 + \textcolor{b l u e}{1} , 1 + \textcolor{red}{2}\right) = p \left(8 , 3\right)$