# What is the slope of the line passing through the following points: (5,3) , (–5, 5) ?

May 29, 2018

$\implies - \frac{1}{5}$

#### Explanation:

Slope in two dimensions is defined as the relative change in one dimension compared to the change in the other dimension.

Specifically for 2D Cartesian coordinates, we define slope $m$ as:

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

given two points ${\text{P}}_{1} \left({x}_{1} , {y}_{1}\right)$ and ${\text{P}}_{2} \left({x}_{2} , {y}_{2}\right)$.

In this problem we are given ${\text{P}}_{1} = \left(5 , 3\right)$ and ${\text{P}}_{2} = \left(- 5 , 5\right)$

$m = \frac{5 - 3}{- 5 - 5} = \frac{2}{- 10} = - \frac{1}{5}$

May 29, 2018

$m = - \frac{1}{5}$

#### Explanation:

After the formula
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

we get
$m = \frac{5 - 3}{- 5 - 5} = - \frac{2}{10} = - \frac{1}{5}$