# How do you determine if the lines through the given points (3,2), (5,8) are parallel and which, if any, are perpendicular?

See hint below

#### Explanation:

HINT:

The slope $m$ of the line parallel to the line passing through the given points $\left({x}_{1} , {y}_{1}\right) \setminus \equiv \left(3 , 2\right)$ & $\left({x}_{2} , {y}_{2}\right) \setminus \equiv \left(5 , 8\right)$ is given as

$m = \setminus \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$= \setminus \frac{8 - 2}{5 - 3}$

$= 3$

The slope $m$ of the line perpendicular to the line passing through the given points $\left({x}_{1} , {y}_{1}\right) \setminus \equiv \left(3 , 2\right)$ & $\left({x}_{2} , {y}_{2}\right) \setminus \equiv \left(5 , 8\right)$ is given as

$m = - \frac{1}{\setminus \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}}$

$= - \frac{1}{\setminus} \frac{8 - 2}{5 - 3}$

$= - \frac{1}{3}$