# How do you find the slope for (2,4) and (4,-2)?

Sep 11, 2015

Slope of the line joining $\left(2 , 4\right)$ and $\left(4 , - 2\right)$ is $- 3$

#### Explanation:

Given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ the slope between them is defined to be:
$\textcolor{w h i t e}{\text{XXX}} m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For the given points $\left(\textcolor{red}{2 , 4}\right)$ and $\left(\textcolor{b l u e}{4 , - 2}\right)$, this becomes
$\textcolor{w h i t e}{\text{XXX}} m = \frac{\textcolor{b l u e}{\left(- 2\right)} - \textcolor{red}{4}}{\textcolor{b l u e}{4} - \textcolor{red}{2}} = \frac{- 6}{2} = - 3$

Sep 11, 2015

$= - 3$

#### Explanation:

${x}_{1} = 2$
${y}_{1} = 4$
${x}_{2} = 4$
${y}_{2} = - 2$

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
$m = \frac{- 2 - 4}{4 - 2} = \frac{- 6}{2} = - 3$