# How do you find the slope of any line parallel to the line through points (19, 1) and (10, 2)?

Jun 24, 2015

All lines parallel to a line through the points $\left(19 , 1\right)$ and $\left(10 , 2\right)$ will have a slope of $\left(- \frac{1}{9}\right)$

#### Explanation:

All parallel lines have the same slope.

Given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ the slope of the line through those points is (by definition)
$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For the given data points this becomes:
$m = \frac{2 - 1}{1 - 19} = - \frac{1}{9}$